%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP087^2 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:55:27 AM UTC 2026
% Result : Theorem 3.08s 1.95s
% Output : Refutation 3.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ITP087^2 : TPTP v9.2.1. Released v7.5.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n014.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 08:26:12 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.45 ---- Original DTF file ---
% 0.30/0.45 thf(spec,logic,$$dhol).
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 % File : ITP087^2 : TPTP v9.2.1. Released v7.5.0.
% 0.30/0.45 % Domain : Interactive Theorem Proving
% 0.30/0.45 % Problem : Sledgehammer KnowledgeKeysSecrets problem prob_277__3294194_1
% 0.30/0.45 % Version : Especial.
% 0.30/0.45 % English :
% 0.30/0.45
% 0.30/0.45 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.30/0.45 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.30/0.45 % Source : [Des21]
% 0.30/0.45 % Names : KnowledgeKeysSecrets/prob_277__3294194_1 [Des21]
% 0.30/0.45
% 0.30/0.45 % Status : Theorem
% 0.30/0.45 % Rating : 0.00 v9.1.0, 0.33 v9.0.0, 0.00 v7.5.0
% 0.30/0.45 % Syntax : Number of formulae : 350 ( 110 unt; 65 typ; 0 def)
% 0.30/0.45 % Number of atoms : 1072 ( 276 equ; 0 cnn)
% 0.30/0.45 % Maximal formula atoms : 13 ( 3 avg)
% 0.30/0.45 % Number of connectives : 4567 ( 205 ~; 36 |; 96 &;3683 @)
% 0.30/0.45 % ( 0 <=>; 547 =>; 0 <=; 0 <~>)
% 0.30/0.45 % Maximal formula depth : 20 ( 8 avg)
% 0.30/0.45 % Number of types : 8 ( 7 usr)
% 0.30/0.45 % Number of type conns : 114 ( 114 >; 0 *; 0 +; 0 <<)
% 0.30/0.45 % Number of symbols : 59 ( 58 usr; 5 con; 0-3 aty)
% 0.30/0.45 % Number of variables : 977 ( 64 ^; 864 !; 30 ?; 977 :)
% 0.30/0.45 % ( 19 !>; 0 ?*; 0 @-; 0 @+)
% 0.30/0.45 % SPC : TH1_THM_EQU_NAR
% 0.30/0.45
% 0.30/0.45 % Comments : This file was generated by Sledgehammer 2021-02-23 16:19:38.787
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 % Could-be-implicit typings (9)
% 0.30/0.45 thf(ty_t_Secrecy__types_OExpression,type,
% 0.30/0.45 secrecy_Expression: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_t_Secrecy__types_OSecrets,type,
% 0.30/0.45 secrecy_Secrets: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_t_Secrecy__types_OspecID,type,
% 0.30/0.45 secrecy_specID: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_t_Secrecy__types_OchanID,type,
% 0.30/0.45 secrecy_chanID: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_t_Secrecy__types_OKeys,type,
% 0.30/0.45 secrecy_Keys: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_t_Secrecy__types_OKS,type,
% 0.30/0.45 secrecy_KS: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_t_List_Olist,type,
% 0.30/0.45 list: $tType > $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_t_Set_Oset,type,
% 0.30/0.45 set: $tType > $tType ).
% 0.30/0.45
% 0.30/0.45 thf(ty_t_Nat_Onat,type,
% 0.30/0.45 nat: $tType ).
% 0.30/0.45
% 0.30/0.45 % Explicit typings (56)
% 0.30/0.45 thf(sy_cl_Lattices_Obounded__lattice,type,
% 0.30/0.45 bounded_lattice:
% 0.30/0.45 !>[A: $tType] : $o ).
% 0.30/0.45
% 0.30/0.45 thf(sy_cl_HOL_Otype,type,
% 0.30/0.45 type:
% 0.30/0.45 !>[A: $tType] : $o ).
% 0.30/0.45
% 0.30/0.45 thf(sy_cl_Orderings_Obot,type,
% 0.30/0.45 bot:
% 0.30/0.45 !>[A: $tType] : $o ).
% 0.30/0.45
% 0.30/0.45 thf(sy_cl_Orderings_Oord,type,
% 0.30/0.45 ord:
% 0.30/0.45 !>[A: $tType] : $o ).
% 0.30/0.45
% 0.30/0.45 thf(sy_cl_Orderings_Oorder,type,
% 0.30/0.45 order:
% 0.30/0.45 !>[A: $tType] : $o ).
% 0.30/0.45
% 0.30/0.45 thf(sy_cl_Orderings_Olinorder,type,
% 0.30/0.45 linorder:
% 0.30/0.45 !>[A: $tType] : $o ).
% 0.30/0.45
% 0.30/0.45 thf(sy_cl_Orderings_Opreorder,type,
% 0.30/0.45 preorder:
% 0.30/0.45 !>[A: $tType] : $o ).
% 0.30/0.45
% 0.30/0.45 thf(sy_cl_Orderings_Oorder__bot,type,
% 0.30/0.45 order_bot:
% 0.30/0.45 !>[A: $tType] : $o ).
% 0.30/0.45
% 0.30/0.45 thf(sy_cl_Lattices_Obounded__semilattice__sup__bot,type,
% 0.30/0.45 bounde1808546759up_bot:
% 0.30/0.45 !>[A: $tType] : $o ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_CompLocalSecrets_OLocalSecrets,type,
% 0.30/0.45 localSecrets: secrecy_specID > ( set @ secrecy_KS ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__khazhniute_OeoutKnowCorrect,type,
% 0.30/0.45 knowle1667810483orrect: secrecy_specID > secrecy_KS > $o ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__khazhniute_Oknow,type,
% 0.30/0.45 knowle1437066798e_know: secrecy_specID > secrecy_KS > $o ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Lattices_Osup__class_Osup,type,
% 0.30/0.45 sup_sup:
% 0.30/0.45 !>[A: $tType] : ( A > A > A ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_ListExtras_Omem,type,
% 0.30/0.45 mem:
% 0.30/0.45 !>[A: $tType] : ( A > ( list @ A ) > $o ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Orderings_Obot__class_Obot,type,
% 0.30/0.45 bot_bot:
% 0.30/0.45 !>[A: $tType] : A ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.30/0.45 ord_less_eq:
% 0.30/0.45 !>[A: $tType] : ( A > A > $o ) ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Secrecy_OcorrectCompositionKS,type,
% 0.30/0.45 correctCompositionKS: secrecy_specID > $o ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Secrecy_OcorrectCompositionKeys,type,
% 0.30/0.45 correc17873122onKeys: secrecy_specID > $o ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Secrecy_Oeout,type,
% 0.30/0.45 eout: secrecy_specID > secrecy_Expression > $o ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Secrecy_OeoutM,type,
% 0.30/0.45 eoutM: secrecy_specID > ( set @ secrecy_chanID ) > secrecy_Expression > $o ).
% 0.30/0.45
% 0.30/0.45 thf(sy_c_Secrecy_OexprChannel,type,
% 0.30/0.45 exprChannel: secrecy_chanID > secrecy_Expression > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Secrecy_Oine,type,
% 0.30/0.46 ine: secrecy_specID > secrecy_Expression > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Secrecy_OineM,type,
% 0.30/0.46 ineM: secrecy_specID > ( set @ secrecy_chanID ) > secrecy_Expression > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Secrecy_Oine__exprChannelSet,type,
% 0.30/0.46 ine_exprChannelSet: secrecy_specID > ( set @ secrecy_chanID ) > secrecy_Expression > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Secrecy_Oine__exprChannelSingle,type,
% 0.30/0.46 ine_ex1303305700Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Secrecy_OnotSpecKeysSecretsExpr,type,
% 0.30/0.46 notSpe1586871396tsExpr: secrecy_specID > ( list @ secrecy_Expression ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Secrecy_Oout__exprChannelSet,type,
% 0.30/0.46 out_exprChannelSet: secrecy_specID > ( set @ secrecy_chanID ) > secrecy_Expression > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Secrecy_Oout__exprChannelSingle,type,
% 0.30/0.46 out_ex985543062Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Secrecy_OspecKeys,type,
% 0.30/0.46 specKeys: secrecy_specID > ( set @ secrecy_Keys ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Secrecy_OspecKeysSecrets,type,
% 0.30/0.46 specKeysSecrets: secrecy_specID > ( set @ secrecy_KS ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Secrecy_OspecSecrets,type,
% 0.30/0.46 specSecrets: secrecy_specID > ( set @ secrecy_Secrets ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Secrecy__types_OExpression_OkE,type,
% 0.30/0.46 secrecy_kE: secrecy_Keys > secrecy_Expression ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Secrecy__types_OExpression_OsE,type,
% 0.30/0.46 secrecy_sE: secrecy_Secrets > secrecy_Expression ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Secrecy__types_OKS2Expression,type,
% 0.30/0.46 secrec1016742679ession: secrecy_KS > secrecy_Expression ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Secrecy__types_OKS_OkKS,type,
% 0.30/0.46 secrecy_kKS: secrecy_Keys > secrecy_KS ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Secrecy__types_OKS_OsKS,type,
% 0.30/0.46 secrecy_sKS: secrecy_Secrets > secrecy_KS ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_OCollect,type,
% 0.30/0.46 collect:
% 0.30/0.46 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_Oinsert,type,
% 0.30/0.46 insert:
% 0.30/0.46 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_Ois__empty,type,
% 0.30/0.46 is_empty:
% 0.30/0.46 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_Ois__singleton,type,
% 0.30/0.46 is_singleton:
% 0.30/0.46 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_Othe__elem,type,
% 0.30/0.46 the_elem:
% 0.30/0.46 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_inout_OcorrectCompositionIn,type,
% 0.30/0.46 correctCompositionIn: secrecy_specID > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_inout_OcorrectCompositionLoc,type,
% 0.30/0.46 correc965049635ionLoc: secrecy_specID > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_inout_OcorrectCompositionOut,type,
% 0.30/0.46 correc990227761ionOut: secrecy_specID > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_inout_OinStream,type,
% 0.30/0.46 inStream: secrecy_specID > ( set @ secrecy_chanID ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_inout_Oins,type,
% 0.30/0.46 ins: secrecy_specID > ( set @ secrecy_chanID ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_inout_Oloc,type,
% 0.30/0.46 loc: secrecy_specID > ( set @ secrecy_chanID ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_inout_OlocStream,type,
% 0.30/0.46 locStream: secrecy_specID > ( set @ secrecy_chanID ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_inout_Oout,type,
% 0.30/0.46 out: secrecy_specID > ( set @ secrecy_chanID ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_inout_Osubcomponents,type,
% 0.30/0.46 subcomponents: secrecy_specID > ( set @ secrecy_specID ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_member,type,
% 0.30/0.46 member:
% 0.30/0.46 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_P,type,
% 0.30/0.46 p: secrecy_specID ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_PQ,type,
% 0.30/0.46 pq: secrecy_specID ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_Q,type,
% 0.30/0.46 q: secrecy_specID ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_key____,type,
% 0.30/0.46 key: secrecy_Keys ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_m,type,
% 0.30/0.46 m: secrecy_KS ).
% 0.30/0.46
% 0.30/0.46 % Relevant facts (256)
% 0.30/0.46 thf(fact_0_cCompKS,axiom,
% 0.30/0.46 correctCompositionKS @ pq ).
% 0.30/0.46
% 0.30/0.46 % cCompKS
% 0.30/0.46 thf(fact_1_notKSQ,axiom,
% 0.30/0.46 ~ ( member @ secrecy_KS @ m @ ( specKeysSecrets @ q ) ) ).
% 0.30/0.46
% 0.30/0.46 % notKSQ
% 0.30/0.46 thf(fact_2_notKSP,axiom,
% 0.30/0.46 ~ ( member @ secrecy_KS @ m @ ( specKeysSecrets @ p ) ) ).
% 0.30/0.46
% 0.30/0.46 % notKSP
% 0.30/0.46 thf(fact_3_subPQ,axiom,
% 0.30/0.46 ( ( subcomponents @ pq )
% 0.30/0.46 = ( insert @ secrecy_specID @ p @ ( insert @ secrecy_specID @ q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subPQ
% 0.30/0.46 thf(fact_4_cCompI,axiom,
% 0.30/0.46 correctCompositionIn @ pq ).
% 0.30/0.46
% 0.30/0.46 % cCompI
% 0.30/0.46 thf(fact_5_assms_I3_J,axiom,
% 0.30/0.46 knowle1437066798e_know @ p @ m ).
% 0.30/0.46
% 0.30/0.46 % assms(3)
% 0.30/0.46 thf(fact_6_a1,axiom,
% 0.30/0.46 ( m
% 0.30/0.46 = ( secrecy_kKS @ key ) ) ).
% 0.30/0.46
% 0.30/0.46 % a1
% 0.30/0.46 thf(fact_7_correctCompositionKS__PQ,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correctCompositionKS @ PQ )
% 0.30/0.46 => ( ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 0.30/0.46 => ( ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 0.30/0.46 | ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % correctCompositionKS_PQ
% 0.30/0.46 thf(fact_8_correctCompositionKS__neg1,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correctCompositionKS @ PQ )
% 0.30/0.46 => ( ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 0.30/0.46 => ( ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) )
% 0.30/0.46 => ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % correctCompositionKS_neg1
% 0.30/0.46 thf(fact_9_correctCompositionKS__negP,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correctCompositionKS @ PQ )
% 0.30/0.46 => ( ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 0.30/0.46 => ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ P ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % correctCompositionKS_negP
% 0.30/0.46 thf(fact_10_correctCompositionKS__negQ,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correctCompositionKS @ PQ )
% 0.30/0.46 => ( ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 0.30/0.46 => ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % correctCompositionKS_negQ
% 0.30/0.46 thf(fact_11_singletonI,axiom,
% 0.30/0.46 ! [A: $tType,A2: A] : ( member @ A @ A2 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % singletonI
% 0.30/0.46 thf(fact_12_KS_Oinject_I1_J,axiom,
% 0.30/0.46 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 0.30/0.46 ( ( ( secrecy_kKS @ X1 )
% 0.30/0.46 = ( secrecy_kKS @ Y1 ) )
% 0.30/0.46 = ( X1 = Y1 ) ) ).
% 0.30/0.46
% 0.30/0.46 % KS.inject(1)
% 0.30/0.46 thf(fact_13_insertCI,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,B: set @ A,B2: A] :
% 0.30/0.46 ( ( ~ ( member @ A @ A2 @ B )
% 0.30/0.46 => ( A2 = B2 ) )
% 0.30/0.46 => ( member @ A @ A2 @ ( insert @ A @ B2 @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insertCI
% 0.30/0.46 thf(fact_14_insert__iff,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,B2: A,A3: set @ A] :
% 0.30/0.46 ( ( member @ A @ A2 @ ( insert @ A @ B2 @ A3 ) )
% 0.30/0.46 = ( ( A2 = B2 )
% 0.30/0.46 | ( member @ A @ A2 @ A3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_iff
% 0.30/0.46 thf(fact_15_insert__absorb2,axiom,
% 0.30/0.46 ! [A: $tType,X: A,A3: set @ A] :
% 0.30/0.46 ( ( insert @ A @ X @ ( insert @ A @ X @ A3 ) )
% 0.30/0.46 = ( insert @ A @ X @ A3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_absorb2
% 0.30/0.46 thf(fact_16_empty__iff,axiom,
% 0.30/0.46 ! [A: $tType,C: A] :
% 0.30/0.46 ~ ( member @ A @ C @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % empty_iff
% 0.30/0.46 thf(fact_17_all__not__in__conv,axiom,
% 0.30/0.46 ! [A: $tType,A3: set @ A] :
% 0.30/0.46 ( ( ! [X2: A] :
% 0.30/0.46 ~ ( member @ A @ X2 @ A3 ) )
% 0.30/0.46 = ( A3
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % all_not_in_conv
% 0.30/0.46 thf(fact_18_Collect__empty__eq,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o] :
% 0.30/0.46 ( ( ( collect @ A @ P )
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 = ( ! [X2: A] :
% 0.30/0.46 ~ ( P @ X2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_empty_eq
% 0.30/0.46 thf(fact_19_empty__Collect__eq,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o] :
% 0.30/0.46 ( ( ( bot_bot @ ( set @ A ) )
% 0.30/0.46 = ( collect @ A @ P ) )
% 0.30/0.46 = ( ! [X2: A] :
% 0.30/0.46 ~ ( P @ X2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % empty_Collect_eq
% 0.30/0.46 thf(fact_20_bot__apply,axiom,
% 0.30/0.46 ! [C2: $tType,D: $tType] :
% 0.30/0.46 ( ( bot @ C2 )
% 0.30/0.46 => ( ( bot_bot @ ( D > C2 ) )
% 0.30/0.46 = ( ^ [X2: D] : ( bot_bot @ C2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot_apply
% 0.30/0.46 thf(fact_21_singletonD,axiom,
% 0.30/0.46 ! [A: $tType,B2: A,A2: A] :
% 0.30/0.46 ( ( member @ A @ B2 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.46 => ( B2 = A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % singletonD
% 0.30/0.46 thf(fact_22_bot__set__def,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( bot_bot @ ( set @ A ) )
% 0.30/0.46 = ( collect @ A @ ( bot_bot @ ( A > $o ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot_set_def
% 0.30/0.46 thf(fact_23_bot__fun__def,axiom,
% 0.30/0.46 ! [B3: $tType,A: $tType] :
% 0.30/0.46 ( ( bot @ B3 )
% 0.30/0.46 => ( ( bot_bot @ ( A > B3 ) )
% 0.30/0.46 = ( ^ [X2: A] : ( bot_bot @ B3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot_fun_def
% 0.30/0.46 thf(fact_24_ex__in__conv,axiom,
% 0.30/0.46 ! [A: $tType,A3: set @ A] :
% 0.30/0.46 ( ( ? [X2: A] : ( member @ A @ X2 @ A3 ) )
% 0.30/0.46 = ( A3
% 0.30/0.46 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ex_in_conv
% 0.30/0.46 thf(fact_25_equals0I,axiom,
% 0.30/0.46 ! [A: $tType,A3: set @ A] :
% 0.30/0.46 ( ! [Y: A] :
% 0.30/0.46 ~ ( member @ A @ Y @ A3 )
% 0.30/0.46 => ( A3
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % equals0I
% 0.30/0.46 thf(fact_26_equals0D,axiom,
% 0.30/0.46 ! [A: $tType,A3: set @ A,A2: A] :
% 0.30/0.46 ( ( A3
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 => ~ ( member @ A @ A2 @ A3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % equals0D
% 0.30/0.46 thf(fact_27_emptyE,axiom,
% 0.30/0.46 ! [A: $tType,A2: A] :
% 0.30/0.46 ~ ( member @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % emptyE
% 0.30/0.46 thf(fact_28_mk__disjoint__insert,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,A3: set @ A] :
% 0.30/0.46 ( ( member @ A @ A2 @ A3 )
% 0.30/0.46 => ? [B4: set @ A] :
% 0.30/0.46 ( ( A3
% 0.30/0.46 = ( insert @ A @ A2 @ B4 ) )
% 0.30/0.46 & ~ ( member @ A @ A2 @ B4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mk_disjoint_insert
% 0.30/0.46 thf(fact_29_insert__commute,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Y2: A,A3: set @ A] :
% 0.30/0.46 ( ( insert @ A @ X @ ( insert @ A @ Y2 @ A3 ) )
% 0.30/0.46 = ( insert @ A @ Y2 @ ( insert @ A @ X @ A3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_commute
% 0.30/0.46 thf(fact_30_insert__eq__iff,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,A3: set @ A,B2: A,B: set @ A] :
% 0.30/0.46 ( ~ ( member @ A @ A2 @ A3 )
% 0.30/0.46 => ( ~ ( member @ A @ B2 @ B )
% 0.30/0.46 => ( ( ( insert @ A @ A2 @ A3 )
% 0.30/0.46 = ( insert @ A @ B2 @ B ) )
% 0.30/0.46 = ( ( ( A2 = B2 )
% 0.30/0.46 => ( A3 = B ) )
% 0.30/0.46 & ( ( A2 != B2 )
% 0.30/0.46 => ? [C3: set @ A] :
% 0.30/0.46 ( ( A3
% 0.30/0.46 = ( insert @ A @ B2 @ C3 ) )
% 0.30/0.46 & ~ ( member @ A @ B2 @ C3 )
% 0.30/0.46 & ( B
% 0.30/0.46 = ( insert @ A @ A2 @ C3 ) )
% 0.30/0.46 & ~ ( member @ A @ A2 @ C3 ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_eq_iff
% 0.30/0.46 thf(fact_31_insert__absorb,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,A3: set @ A] :
% 0.30/0.46 ( ( member @ A @ A2 @ A3 )
% 0.30/0.46 => ( ( insert @ A @ A2 @ A3 )
% 0.30/0.46 = A3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_absorb
% 0.30/0.46 thf(fact_32_insert__ident,axiom,
% 0.30/0.46 ! [A: $tType,X: A,A3: set @ A,B: set @ A] :
% 0.30/0.46 ( ~ ( member @ A @ X @ A3 )
% 0.30/0.46 => ( ~ ( member @ A @ X @ B )
% 0.30/0.46 => ( ( ( insert @ A @ X @ A3 )
% 0.30/0.46 = ( insert @ A @ X @ B ) )
% 0.30/0.46 = ( A3 = B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_ident
% 0.30/0.46 thf(fact_33_Set_Oset__insert,axiom,
% 0.30/0.46 ! [A: $tType,X: A,A3: set @ A] :
% 0.30/0.46 ( ( member @ A @ X @ A3 )
% 0.30/0.46 => ~ ! [B4: set @ A] :
% 0.30/0.46 ( ( A3
% 0.30/0.46 = ( insert @ A @ X @ B4 ) )
% 0.30/0.46 => ( member @ A @ X @ B4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Set.set_insert
% 0.30/0.46 thf(fact_34_insertI2,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,B: set @ A,B2: A] :
% 0.30/0.46 ( ( member @ A @ A2 @ B )
% 0.30/0.46 => ( member @ A @ A2 @ ( insert @ A @ B2 @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insertI2
% 0.30/0.46 thf(fact_35_insertI1,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,B: set @ A] : ( member @ A @ A2 @ ( insert @ A @ A2 @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 % insertI1
% 0.30/0.46 thf(fact_36_insertE,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,B2: A,A3: set @ A] :
% 0.30/0.46 ( ( member @ A @ A2 @ ( insert @ A @ B2 @ A3 ) )
% 0.30/0.46 => ( ( A2 != B2 )
% 0.30/0.46 => ( member @ A @ A2 @ A3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insertE
% 0.30/0.46 thf(fact_37_singleton__inject,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,B2: A] :
% 0.30/0.46 ( ( ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 = ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.46 => ( A2 = B2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % singleton_inject
% 0.30/0.46 thf(fact_38_insert__not__empty,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,A3: set @ A] :
% 0.30/0.46 ( ( insert @ A @ A2 @ A3 )
% 0.30/0.46 != ( bot_bot @ ( set @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_not_empty
% 0.30/0.46 thf(fact_39_doubleton__eq__iff,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,B2: A,C: A,D2: A] :
% 0.30/0.46 ( ( ( insert @ A @ A2 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.46 = ( insert @ A @ C @ ( insert @ A @ D2 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.30/0.46 = ( ( ( A2 = C )
% 0.30/0.46 & ( B2 = D2 ) )
% 0.30/0.46 | ( ( A2 = D2 )
% 0.30/0.46 & ( B2 = C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % doubleton_eq_iff
% 0.30/0.46 thf(fact_40_singleton__iff,axiom,
% 0.30/0.46 ! [A: $tType,B2: A,A2: A] :
% 0.30/0.46 ( ( member @ A @ B2 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.46 = ( B2 = A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % singleton_iff
% 0.30/0.46 thf(fact_41_the__elem__eq,axiom,
% 0.30/0.46 ! [A: $tType,X: A] :
% 0.30/0.46 ( ( the_elem @ A @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.46 = X ) ).
% 0.30/0.46
% 0.30/0.46 % the_elem_eq
% 0.30/0.46 thf(fact_42_is__singletonI,axiom,
% 0.30/0.46 ! [A: $tType,X: A] : ( is_singleton @ A @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % is_singletonI
% 0.30/0.46 thf(fact_43_a11,axiom,
% 0.30/0.46 ine @ p @ ( secrecy_kE @ key ) ).
% 0.30/0.46
% 0.30/0.46 % a11
% 0.30/0.46 thf(fact_44_TBtheorem3b,axiom,
% 0.30/0.46 ! [P: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.30/0.46 ( ~ ( ineM @ P @ M @ E )
% 0.30/0.46 => ( ~ ( ineM @ Q @ M @ E )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ~ ( ineM @ PQ @ M @ E ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem3b
% 0.30/0.46 thf(fact_45_mem__Collect__eq,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,P: A > $o] :
% 0.30/0.46 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.30/0.46 = ( P @ A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % mem_Collect_eq
% 0.30/0.46 thf(fact_46_Collect__mem__eq,axiom,
% 0.30/0.46 ! [A: $tType,A3: set @ A] :
% 0.30/0.46 ( ( collect @ A
% 0.30/0.46 @ ^ [X2: A] : ( member @ A @ X2 @ A3 ) )
% 0.30/0.46 = A3 ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_mem_eq
% 0.30/0.46 thf(fact_47_Collect__cong,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.30/0.46 ( ! [X3: A] :
% 0.30/0.46 ( ( P @ X3 )
% 0.30/0.46 = ( Q @ X3 ) )
% 0.30/0.46 => ( ( collect @ A @ P )
% 0.30/0.46 = ( collect @ A @ Q ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_cong
% 0.30/0.46 thf(fact_48_ext,axiom,
% 0.30/0.46 ! [B3: $tType,A: $tType,F: A > B3,G: A > B3] :
% 0.30/0.46 ( ! [X3: A] :
% 0.30/0.46 ( ( F @ X3 )
% 0.30/0.46 = ( G @ X3 ) )
% 0.30/0.46 => ( F = G ) ) ).
% 0.30/0.46
% 0.30/0.46 % ext
% 0.30/0.46 thf(fact_49_TBtheorem1b,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.30/0.46 ( ( ineM @ PQ @ M @ E )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ( ( ineM @ P @ M @ E )
% 0.30/0.46 | ( ineM @ Q @ M @ E ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem1b
% 0.30/0.46 thf(fact_50_a11ext,axiom,
% 0.30/0.46 ( ( ine @ p @ ( secrecy_kE @ key ) )
% 0.30/0.46 | ( ine @ q @ ( secrecy_kE @ key ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % a11ext
% 0.30/0.46 thf(fact_51_Set_Ois__empty__def,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( is_empty @ A )
% 0.30/0.46 = ( ^ [A4: set @ A] :
% 0.30/0.46 ( A4
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Set.is_empty_def
% 0.30/0.46 thf(fact_52_correctCompositionIn__prop1,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,X: secrecy_chanID] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ( ( member @ secrecy_chanID @ X @ ( ins @ PQ ) )
% 0.30/0.46 => ( ( member @ secrecy_chanID @ X @ ( ins @ P ) )
% 0.30/0.46 | ( member @ secrecy_chanID @ X @ ( ins @ Q ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % correctCompositionIn_prop1
% 0.30/0.46 thf(fact_53_correctCompositionIn__L2,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 0.30/0.46 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 0.30/0.46 | ( member @ secrecy_chanID @ Ch @ ( ins @ Q ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % correctCompositionIn_L2
% 0.30/0.46 thf(fact_54_is__singleton__def,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( is_singleton @ A )
% 0.30/0.46 = ( ^ [A4: set @ A] :
% 0.30/0.46 ? [X2: A] :
% 0.30/0.46 ( A4
% 0.30/0.46 = ( insert @ A @ X2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % is_singleton_def
% 0.30/0.46 thf(fact_55_Expression_Oinject_I1_J,axiom,
% 0.30/0.46 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 0.30/0.46 ( ( ( secrecy_kE @ X1 )
% 0.30/0.46 = ( secrecy_kE @ Y1 ) )
% 0.30/0.46 = ( X1 = Y1 ) ) ).
% 0.30/0.46
% 0.30/0.46 % Expression.inject(1)
% 0.30/0.46 thf(fact_56_not__ine__ineM,axiom,
% 0.30/0.46 ! [P: secrecy_specID,E: secrecy_Expression,M: set @ secrecy_chanID] :
% 0.30/0.46 ( ~ ( ine @ P @ E )
% 0.30/0.46 => ~ ( ineM @ P @ M @ E ) ) ).
% 0.30/0.46
% 0.30/0.46 % not_ine_ineM
% 0.30/0.46 thf(fact_57_ineM__ine,axiom,
% 0.30/0.46 ! [P: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression] :
% 0.30/0.46 ( ( ineM @ P @ M @ E )
% 0.30/0.46 => ( ine @ P @ E ) ) ).
% 0.30/0.46
% 0.30/0.46 % ineM_ine
% 0.30/0.46 thf(fact_58_not__know__k__not__ine,axiom,
% 0.30/0.46 ! [A3: secrecy_specID,M2: secrecy_Keys] :
% 0.30/0.46 ( ~ ( knowle1437066798e_know @ A3 @ ( secrecy_kKS @ M2 ) )
% 0.30/0.46 => ~ ( ine @ A3 @ ( secrecy_kE @ M2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % not_know_k_not_ine
% 0.30/0.46 thf(fact_59_is__singleton__the__elem,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( is_singleton @ A )
% 0.30/0.46 = ( ^ [A4: set @ A] :
% 0.30/0.46 ( A4
% 0.30/0.46 = ( insert @ A @ ( the_elem @ A @ A4 ) @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % is_singleton_the_elem
% 0.30/0.46 thf(fact_60_is__singletonI_H,axiom,
% 0.30/0.46 ! [A: $tType,A3: set @ A] :
% 0.30/0.46 ( ( A3
% 0.30/0.46 != ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 => ( ! [X3: A,Y: A] :
% 0.30/0.46 ( ( member @ A @ X3 @ A3 )
% 0.30/0.46 => ( ( member @ A @ Y @ A3 )
% 0.30/0.46 => ( X3 = Y ) ) )
% 0.30/0.46 => ( is_singleton @ A @ A3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % is_singletonI'
% 0.30/0.46 thf(fact_61_TBtheorem1a,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.30/0.46 ( ( ine @ PQ @ E )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ( ( ine @ P @ E )
% 0.30/0.46 | ( ine @ Q @ E ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem1a
% 0.30/0.46 thf(fact_62_TBtheorem3a,axiom,
% 0.30/0.46 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.30/0.46 ( ~ ( ine @ P @ E )
% 0.30/0.46 => ( ~ ( ine @ Q @ E )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ~ ( ine @ PQ @ E ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem3a
% 0.30/0.46 thf(fact_63_is__singletonE,axiom,
% 0.30/0.46 ! [A: $tType,A3: set @ A] :
% 0.30/0.46 ( ( is_singleton @ A @ A3 )
% 0.30/0.46 => ~ ! [X3: A] :
% 0.30/0.46 ( A3
% 0.30/0.46 != ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % is_singletonE
% 0.30/0.46 thf(fact_64_bot__empty__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( bot_bot @ ( A > $o ) )
% 0.30/0.46 = ( ^ [X2: A] : ( member @ A @ X2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot_empty_eq
% 0.30/0.46 thf(fact_65_Collect__empty__eq__bot,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o] :
% 0.30/0.46 ( ( ( collect @ A @ P )
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 = ( P
% 0.30/0.46 = ( bot_bot @ ( A > $o ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_empty_eq_bot
% 0.30/0.46 thf(fact_66_TBlemma3b,axiom,
% 0.30/0.46 ! [P: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID,Ch: secrecy_chanID] :
% 0.30/0.46 ( ~ ( ineM @ P @ M @ E )
% 0.30/0.46 => ( ~ ( ineM @ Q @ M @ E )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ( ( member @ secrecy_chanID @ Ch @ M )
% 0.30/0.46 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 0.30/0.46 => ~ ( exprChannel @ Ch @ E ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBlemma3b
% 0.30/0.46 thf(fact_67_correctCompositionIn__L1,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ( ~ ( member @ secrecy_chanID @ Ch @ ( loc @ PQ ) )
% 0.30/0.46 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 0.30/0.46 => ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % correctCompositionIn_L1
% 0.30/0.46 thf(fact_68_KS2Expression_Osimps_I1_J,axiom,
% 0.30/0.46 ! [M2: secrecy_Keys] :
% 0.30/0.46 ( ( secrec1016742679ession @ ( secrecy_kKS @ M2 ) )
% 0.30/0.46 = ( secrecy_kE @ M2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % KS2Expression.simps(1)
% 0.30/0.46 thf(fact_69_TBtheorem4a__empty,axiom,
% 0.30/0.46 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.30/0.46 ( ( ( ine @ P @ E )
% 0.30/0.46 | ( ine @ Q @ E ) )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ( ( ( loc @ PQ )
% 0.30/0.46 = ( bot_bot @ ( set @ secrecy_chanID ) ) )
% 0.30/0.46 => ( ine @ PQ @ E ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem4a_empty
% 0.30/0.46 thf(fact_70_know_Osimps_I1_J,axiom,
% 0.30/0.46 ! [A3: secrecy_specID,M2: secrecy_Keys] :
% 0.30/0.46 ( ( knowle1437066798e_know @ A3 @ ( secrecy_kKS @ M2 ) )
% 0.30/0.46 = ( ( ine @ A3 @ ( secrecy_kE @ M2 ) )
% 0.30/0.46 | ( member @ secrecy_KS @ ( secrecy_kKS @ M2 ) @ ( localSecrets @ A3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % know.simps(1)
% 0.30/0.46 thf(fact_71_correctCompositionKS__exprChannel__k__P,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correctCompositionKS @ PQ )
% 0.30/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 0.30/0.46 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 0.30/0.46 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 0.30/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 0.30/0.46 & ( exprChannel @ Ch @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % correctCompositionKS_exprChannel_k_P
% 0.30/0.46 thf(fact_72_LocalSecretsComposition__neg__loc__k,axiom,
% 0.30/0.46 ! [Key: secrecy_Keys,P: secrecy_specID,Ch: secrecy_chanID] :
% 0.30/0.46 ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ P ) )
% 0.30/0.46 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 0.30/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ P ) )
% 0.30/0.46 => ~ ( member @ secrecy_chanID @ Ch @ ( loc @ P ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % LocalSecretsComposition_neg_loc_k
% 0.30/0.46 thf(fact_73_LocalSecretsComposition1,axiom,
% 0.30/0.46 ! [Ls: secrecy_KS,P: secrecy_specID,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.30/0.46 ( ( member @ secrecy_KS @ Ls @ ( localSecrets @ P ) )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( member @ secrecy_KS @ Ls @ ( localSecrets @ PQ ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % LocalSecretsComposition1
% 0.30/0.46 thf(fact_74_LocalSecretsComposition__exprChannel__k,axiom,
% 0.30/0.46 ! [X: secrecy_chanID,Keys: secrecy_Keys,P: secrecy_specID,Q: secrecy_specID] :
% 0.30/0.46 ( ( exprChannel @ X @ ( secrecy_kE @ Keys ) )
% 0.30/0.46 => ( ~ ( ine @ P @ ( secrecy_kE @ Keys ) )
% 0.30/0.46 => ( ~ ( ine @ Q @ ( secrecy_kE @ Keys ) )
% 0.30/0.46 => ( ~ ( member @ secrecy_chanID @ X @ ( ins @ P ) )
% 0.30/0.46 & ~ ( member @ secrecy_chanID @ X @ ( ins @ Q ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % LocalSecretsComposition_exprChannel_k
% 0.30/0.46 thf(fact_75_ine__def,axiom,
% 0.30/0.46 ( ine
% 0.30/0.46 = ( ^ [SP: secrecy_specID,E2: secrecy_Expression] :
% 0.30/0.46 ? [Ch2: secrecy_chanID] :
% 0.30/0.46 ( ( member @ secrecy_chanID @ Ch2 @ ( ins @ SP ) )
% 0.30/0.46 & ( exprChannel @ Ch2 @ E2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ine_def
% 0.30/0.46 thf(fact_76_ine__ins__neg1,axiom,
% 0.30/0.46 ! [P: secrecy_specID,M2: secrecy_Expression,X: secrecy_chanID] :
% 0.30/0.46 ( ~ ( ine @ P @ M2 )
% 0.30/0.46 => ( ( exprChannel @ X @ M2 )
% 0.30/0.46 => ~ ( member @ secrecy_chanID @ X @ ( ins @ P ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ine_ins_neg1
% 0.30/0.46 thf(fact_77_ineM__L1,axiom,
% 0.30/0.46 ! [Ch: secrecy_chanID,M: set @ secrecy_chanID,P: secrecy_specID,E: secrecy_Expression] :
% 0.30/0.46 ( ( member @ secrecy_chanID @ Ch @ M )
% 0.30/0.46 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 0.30/0.46 => ( ( exprChannel @ Ch @ E )
% 0.30/0.46 => ( ineM @ P @ M @ E ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ineM_L1
% 0.30/0.46 thf(fact_78_ineM__def,axiom,
% 0.30/0.46 ( ineM
% 0.30/0.46 = ( ^ [SP: secrecy_specID,M3: set @ secrecy_chanID,E2: secrecy_Expression] :
% 0.30/0.46 ? [Ch2: secrecy_chanID] :
% 0.30/0.46 ( ( member @ secrecy_chanID @ Ch2 @ ( ins @ SP ) )
% 0.30/0.46 & ( member @ secrecy_chanID @ Ch2 @ M3 )
% 0.30/0.46 & ( exprChannel @ Ch2 @ E2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ineM_def
% 0.30/0.46 thf(fact_79_correctCompositionInLoc__exprChannel,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID,M2: secrecy_Expression] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 0.30/0.46 => ( ( exprChannel @ Ch @ M2 )
% 0.30/0.46 => ( ! [X3: secrecy_chanID] :
% 0.30/0.46 ( ( member @ secrecy_chanID @ X3 @ ( ins @ PQ ) )
% 0.30/0.46 => ~ ( exprChannel @ X3 @ M2 ) )
% 0.30/0.46 => ( member @ secrecy_chanID @ Ch @ ( loc @ PQ ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % correctCompositionInLoc_exprChannel
% 0.30/0.46 thf(fact_80_TBtheorem4a__PQ,axiom,
% 0.30/0.46 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.30/0.46 ( ( ( ine @ P @ E )
% 0.30/0.46 | ( ine @ Q @ E ) )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ( ? [Ch3: secrecy_chanID] :
% 0.30/0.46 ( ( ( member @ secrecy_chanID @ Ch3 @ ( ins @ P ) )
% 0.30/0.46 | ( member @ secrecy_chanID @ Ch3 @ ( ins @ Q ) ) )
% 0.30/0.46 & ( exprChannel @ Ch3 @ E )
% 0.30/0.46 & ~ ( member @ secrecy_chanID @ Ch3 @ ( loc @ PQ ) ) )
% 0.30/0.46 => ( ine @ PQ @ E ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem4a_PQ
% 0.30/0.46 thf(fact_81_TBtheorem4a__P,axiom,
% 0.30/0.46 ! [P: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.30/0.46 ( ( ine @ P @ E )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ( ? [Ch3: secrecy_chanID] :
% 0.30/0.46 ( ( member @ secrecy_chanID @ Ch3 @ ( ins @ P ) )
% 0.30/0.46 & ( exprChannel @ Ch3 @ E )
% 0.30/0.46 & ~ ( member @ secrecy_chanID @ Ch3 @ ( loc @ PQ ) ) )
% 0.30/0.46 => ( ine @ PQ @ E ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem4a_P
% 0.30/0.46 thf(fact_82_TBtheorem4b__PQ,axiom,
% 0.30/0.46 ! [P: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.30/0.46 ( ( ( ineM @ P @ M @ E )
% 0.30/0.46 | ( ineM @ Q @ M @ E ) )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ( ? [Ch3: secrecy_chanID] :
% 0.30/0.46 ( ( ( member @ secrecy_chanID @ Ch3 @ ( ins @ P ) )
% 0.30/0.46 | ( member @ secrecy_chanID @ Ch3 @ ( ins @ Q ) ) )
% 0.30/0.46 & ( member @ secrecy_chanID @ Ch3 @ M )
% 0.30/0.46 & ( exprChannel @ Ch3 @ E )
% 0.30/0.46 & ~ ( member @ secrecy_chanID @ Ch3 @ ( loc @ PQ ) ) )
% 0.30/0.46 => ( ineM @ PQ @ M @ E ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem4b_PQ
% 0.30/0.46 thf(fact_83_TBtheorem4b__P,axiom,
% 0.30/0.46 ! [P: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.30/0.46 ( ( ineM @ P @ M @ E )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ( ? [Ch3: secrecy_chanID] :
% 0.30/0.46 ( ( member @ secrecy_chanID @ Ch3 @ ( ins @ Q ) )
% 0.30/0.46 & ( exprChannel @ Ch3 @ E )
% 0.30/0.46 & ~ ( member @ secrecy_chanID @ Ch3 @ ( loc @ PQ ) )
% 0.30/0.46 & ( member @ secrecy_chanID @ Ch3 @ M ) )
% 0.30/0.46 => ( ineM @ PQ @ M @ E ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem4b_P
% 0.30/0.46 thf(fact_84_correctCompositionKS__exprChannel__k__Qex,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correctCompositionKS @ PQ )
% 0.30/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 0.30/0.46 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ Q ) )
% 0.30/0.46 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 0.30/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ? [Ch4: secrecy_chanID] :
% 0.30/0.46 ( ( member @ secrecy_chanID @ Ch4 @ ( ins @ PQ ) )
% 0.30/0.46 & ( exprChannel @ Ch4 @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % correctCompositionKS_exprChannel_k_Qex
% 0.30/0.46 thf(fact_85_correctCompositionKS__exprChannel__k__Pex,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correctCompositionKS @ PQ )
% 0.30/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 0.30/0.46 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 0.30/0.46 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 0.30/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ? [Ch4: secrecy_chanID] :
% 0.30/0.46 ( ( member @ secrecy_chanID @ Ch4 @ ( ins @ PQ ) )
% 0.30/0.46 & ( exprChannel @ Ch4 @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % correctCompositionKS_exprChannel_k_Pex
% 0.30/0.46 thf(fact_86_correctCompositionKS__exprChannel__k__Q,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correctCompositionKS @ PQ )
% 0.30/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 0.30/0.46 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ Q ) )
% 0.30/0.46 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 0.30/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 0.30/0.46 & ( exprChannel @ Ch @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % correctCompositionKS_exprChannel_k_Q
% 0.30/0.46 thf(fact_87_TBtheorem4b__notP1,axiom,
% 0.30/0.46 ! [P: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.30/0.46 ( ( ineM @ P @ M @ E )
% 0.30/0.46 => ( ~ ( ineM @ Q @ M @ E )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ( ? [Ch3: secrecy_chanID] :
% 0.30/0.46 ( ( ine_ex1303305700Single @ P @ Ch3 @ E )
% 0.30/0.46 & ( member @ secrecy_chanID @ Ch3 @ M )
% 0.30/0.46 & ( member @ secrecy_chanID @ Ch3 @ ( loc @ PQ ) ) )
% 0.30/0.46 => ~ ( ineM @ PQ @ M @ E ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem4b_notP1
% 0.30/0.46 thf(fact_88_TBtheorem4a__notP1,axiom,
% 0.30/0.46 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.30/0.46 ( ( ine @ P @ E )
% 0.30/0.46 => ( ~ ( ine @ Q @ E )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ( ? [Ch3: secrecy_chanID] :
% 0.30/0.46 ( ( ine_ex1303305700Single @ P @ Ch3 @ E )
% 0.30/0.46 & ( member @ secrecy_chanID @ Ch3 @ ( loc @ PQ ) ) )
% 0.30/0.46 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem4a_notP1
% 0.30/0.46 thf(fact_89_LocalSecretsComposition__neg1__k,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Keys: secrecy_Keys] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correc965049635ionLoc @ PQ )
% 0.30/0.46 => ( ~ ( ine @ P @ ( secrecy_kE @ Keys ) )
% 0.30/0.46 => ( ~ ( ine @ Q @ ( secrecy_kE @ Keys ) )
% 0.30/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ P ) )
% 0.30/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ Q ) )
% 0.30/0.46 => ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % LocalSecretsComposition_neg1_k
% 0.30/0.46 thf(fact_90_LocalSecretsComposition__ine2__k,axiom,
% 0.30/0.46 ! [K: secrecy_Keys,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 0.30/0.46 ( ( member @ secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ PQ ) )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correc965049635ionLoc @ PQ )
% 0.30/0.46 => ( ~ ( ine @ P @ ( secrecy_kE @ K ) )
% 0.30/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ P ) )
% 0.30/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ Q ) )
% 0.30/0.46 => ( ine @ Q @ ( secrecy_kE @ K ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % LocalSecretsComposition_ine2_k
% 0.30/0.46 thf(fact_91_LocalSecretsComposition__ine1__k,axiom,
% 0.30/0.46 ! [K: secrecy_Keys,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 0.30/0.46 ( ( member @ secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ PQ ) )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correc965049635ionLoc @ PQ )
% 0.30/0.46 => ( ~ ( ine @ Q @ ( secrecy_kE @ K ) )
% 0.30/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ P ) )
% 0.30/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ Q ) )
% 0.30/0.46 => ( ine @ P @ ( secrecy_kE @ K ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % LocalSecretsComposition_ine1_k
% 0.30/0.46 thf(fact_92_TBtheorem4b__notPQ,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set @ secrecy_chanID,E: secrecy_Expression,ChSetQ: set @ secrecy_chanID,M: set @ secrecy_chanID] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ( ( ine_exprChannelSet @ P @ ChSetP @ E )
% 0.30/0.46 => ( ( ine_exprChannelSet @ Q @ ChSetQ @ E )
% 0.30/0.46 => ( ! [X3: secrecy_chanID] :
% 0.30/0.46 ( ( member @ secrecy_chanID @ X3 @ ChSetP )
% 0.30/0.46 => ( member @ secrecy_chanID @ X3 @ ( loc @ PQ ) ) )
% 0.30/0.46 => ( ! [X3: secrecy_chanID] :
% 0.30/0.46 ( ( member @ secrecy_chanID @ X3 @ ChSetQ )
% 0.30/0.46 => ( member @ secrecy_chanID @ X3 @ ( loc @ PQ ) ) )
% 0.30/0.46 => ~ ( ineM @ PQ @ M @ E ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem4b_notPQ
% 0.30/0.46 thf(fact_93_TBtheorem4b__notP2,axiom,
% 0.30/0.46 ! [Q: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set @ secrecy_chanID] :
% 0.30/0.46 ( ~ ( ineM @ Q @ M @ E )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 0.30/0.46 => ( ! [X3: secrecy_chanID] :
% 0.30/0.46 ( ( member @ secrecy_chanID @ X3 @ ChSet )
% 0.30/0.46 => ( member @ secrecy_chanID @ X3 @ ( loc @ PQ ) ) )
% 0.30/0.46 => ~ ( ineM @ PQ @ M @ E ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem4b_notP2
% 0.30/0.46 thf(fact_94_ine__exprChannelSingle__Set,axiom,
% 0.30/0.46 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 0.30/0.46 ( ( ine_ex1303305700Single @ P @ Ch @ E )
% 0.30/0.46 => ( ine_exprChannelSet @ P @ ( insert @ secrecy_chanID @ Ch @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ E ) ) ).
% 0.30/0.46
% 0.30/0.46 % ine_exprChannelSingle_Set
% 0.30/0.46 thf(fact_95_ine__exprChannelSet__Single,axiom,
% 0.30/0.46 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 0.30/0.46 ( ( ine_exprChannelSet @ P @ ( insert @ secrecy_chanID @ Ch @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ E )
% 0.30/0.46 => ( ine_ex1303305700Single @ P @ Ch @ E ) ) ).
% 0.30/0.46
% 0.30/0.46 % ine_exprChannelSet_Single
% 0.30/0.46 thf(fact_96_ine__exprChannelSet__def,axiom,
% 0.30/0.46 ( ine_exprChannelSet
% 0.30/0.46 = ( ^ [SP: secrecy_specID,ChSet2: set @ secrecy_chanID,E2: secrecy_Expression] :
% 0.30/0.46 ( ! [X2: secrecy_chanID] :
% 0.30/0.46 ( ( member @ secrecy_chanID @ X2 @ ChSet2 )
% 0.30/0.46 => ( ( member @ secrecy_chanID @ X2 @ ( ins @ SP ) )
% 0.30/0.46 & ( exprChannel @ X2 @ E2 ) ) )
% 0.30/0.46 & ! [X2: secrecy_chanID] :
% 0.30/0.46 ( ( ~ ( member @ secrecy_chanID @ X2 @ ChSet2 )
% 0.30/0.46 & ( member @ secrecy_chanID @ X2 @ ( ins @ SP ) ) )
% 0.30/0.46 => ~ ( exprChannel @ X2 @ E2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ine_exprChannelSet_def
% 0.30/0.46 thf(fact_97_ine__empty__exprChannelSet,axiom,
% 0.30/0.46 ! [P: secrecy_specID,ChSet: set @ secrecy_chanID,E: secrecy_Expression] :
% 0.30/0.46 ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 0.30/0.46 => ( ( ChSet
% 0.30/0.46 = ( bot_bot @ ( set @ secrecy_chanID ) ) )
% 0.30/0.46 => ~ ( ine @ P @ E ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ine_empty_exprChannelSet
% 0.30/0.46 thf(fact_98_ine__nonempty__exprChannelSet,axiom,
% 0.30/0.46 ! [P: secrecy_specID,ChSet: set @ secrecy_chanID,E: secrecy_Expression] :
% 0.30/0.46 ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 0.30/0.46 => ( ( ChSet
% 0.30/0.46 != ( bot_bot @ ( set @ secrecy_chanID ) ) )
% 0.30/0.46 => ( ine @ P @ E ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ine_nonempty_exprChannelSet
% 0.30/0.46 thf(fact_99_ine__exprChannelSingle__def,axiom,
% 0.30/0.46 ( ine_ex1303305700Single
% 0.30/0.46 = ( ^ [SP: secrecy_specID,Ch2: secrecy_chanID,E2: secrecy_Expression] :
% 0.30/0.46 ( ( member @ secrecy_chanID @ Ch2 @ ( ins @ SP ) )
% 0.30/0.46 & ( exprChannel @ Ch2 @ E2 )
% 0.30/0.46 & ! [X2: secrecy_chanID,T: nat] :
% 0.30/0.46 ( ( ( member @ secrecy_chanID @ X2 @ ( ins @ SP ) )
% 0.30/0.46 & ( X2 != Ch2 ) )
% 0.30/0.46 => ~ ( exprChannel @ X2 @ E2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ine_exprChannelSingle_def
% 0.30/0.46 thf(fact_100_TBtheorem4a__notP2,axiom,
% 0.30/0.46 ! [Q: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set @ secrecy_chanID] :
% 0.30/0.46 ( ~ ( ine @ Q @ E )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 0.30/0.46 => ( ! [X3: secrecy_chanID] :
% 0.30/0.46 ( ( member @ secrecy_chanID @ X3 @ ChSet )
% 0.30/0.46 => ( member @ secrecy_chanID @ X3 @ ( loc @ PQ ) ) )
% 0.30/0.46 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem4a_notP2
% 0.30/0.46 thf(fact_101_TBtheorem4a__notPQ,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set @ secrecy_chanID,E: secrecy_Expression,ChSetQ: set @ secrecy_chanID] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ( ( ine_exprChannelSet @ P @ ChSetP @ E )
% 0.30/0.46 => ( ( ine_exprChannelSet @ Q @ ChSetQ @ E )
% 0.30/0.46 => ( ! [X3: secrecy_chanID] :
% 0.30/0.46 ( ( member @ secrecy_chanID @ X3 @ ChSetP )
% 0.30/0.46 => ( member @ secrecy_chanID @ X3 @ ( loc @ PQ ) ) )
% 0.30/0.46 => ( ! [X3: secrecy_chanID] :
% 0.30/0.46 ( ( member @ secrecy_chanID @ X3 @ ChSetQ )
% 0.30/0.46 => ( member @ secrecy_chanID @ X3 @ ( loc @ PQ ) ) )
% 0.30/0.46 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem4a_notPQ
% 0.30/0.46 thf(fact_102_subcomponents__loc,axiom,
% 0.30/0.46 ! [X: secrecy_specID] :
% 0.30/0.46 ( ( correc965049635ionLoc @ X )
% 0.30/0.46 => ( ( ( subcomponents @ X )
% 0.30/0.46 = ( bot_bot @ ( set @ secrecy_specID ) ) )
% 0.30/0.46 => ( ( loc @ X )
% 0.30/0.46 = ( bot_bot @ ( set @ secrecy_chanID ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subcomponents_loc
% 0.30/0.46 thf(fact_103_LocalSecretsComposition__neg__k,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,M2: secrecy_Keys] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correc965049635ionLoc @ PQ )
% 0.30/0.46 => ( ( correctCompositionKS @ PQ )
% 0.30/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ M2 ) @ ( specKeysSecrets @ P ) )
% 0.30/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ M2 ) @ ( specKeysSecrets @ Q ) )
% 0.30/0.46 => ( ~ ( ine @ P @ ( secrecy_kE @ M2 ) )
% 0.30/0.46 => ( ~ ( ine @ Q @ ( secrecy_kE @ M2 ) )
% 0.30/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ M2 ) @ ( sup_sup @ ( set @ secrecy_KS ) @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 0.30/0.46 => ~ ( member @ secrecy_KS @ ( secrecy_kKS @ M2 ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % LocalSecretsComposition_neg_k
% 0.30/0.46 thf(fact_104_correctCompositionKS__exprChannel__s__P,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correctCompositionKS @ PQ )
% 0.30/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 0.30/0.46 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 0.30/0.46 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 0.30/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 0.30/0.46 & ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % correctCompositionKS_exprChannel_s_P
% 0.30/0.46 thf(fact_105_correctCompositionKS__exprChannel__s__Q,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correctCompositionKS @ PQ )
% 0.30/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 0.30/0.46 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ Q ) )
% 0.30/0.46 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 0.30/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 0.30/0.46 & ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % correctCompositionKS_exprChannel_s_Q
% 0.30/0.46 thf(fact_106_correctCompositionKS__exprChannel__s__Pex,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correctCompositionKS @ PQ )
% 0.30/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 0.30/0.46 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 0.30/0.46 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 0.30/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ? [Ch4: secrecy_chanID] :
% 0.30/0.46 ( ( member @ secrecy_chanID @ Ch4 @ ( ins @ PQ ) )
% 0.30/0.46 & ( exprChannel @ Ch4 @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % correctCompositionKS_exprChannel_s_Pex
% 0.30/0.46 thf(fact_107_UnCI,axiom,
% 0.30/0.46 ! [A: $tType,C: A,B: set @ A,A3: set @ A] :
% 0.30/0.46 ( ( ~ ( member @ A @ C @ B )
% 0.30/0.46 => ( member @ A @ C @ A3 ) )
% 0.30/0.46 => ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A3 @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % UnCI
% 0.30/0.46 thf(fact_108_Un__iff,axiom,
% 0.30/0.46 ! [A: $tType,C: A,A3: set @ A,B: set @ A] :
% 0.30/0.46 ( ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A3 @ B ) )
% 0.30/0.46 = ( ( member @ A @ C @ A3 )
% 0.30/0.46 | ( member @ A @ C @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_iff
% 0.30/0.46 thf(fact_109_KS_Oinject_I2_J,axiom,
% 0.30/0.46 ! [X22: secrecy_Secrets,Y22: secrecy_Secrets] :
% 0.30/0.46 ( ( ( secrecy_sKS @ X22 )
% 0.30/0.46 = ( secrecy_sKS @ Y22 ) )
% 0.30/0.46 = ( X22 = Y22 ) ) ).
% 0.30/0.46
% 0.30/0.46 % KS.inject(2)
% 0.30/0.46 thf(fact_110_Expression_Oinject_I2_J,axiom,
% 0.30/0.46 ! [X22: secrecy_Secrets,Y22: secrecy_Secrets] :
% 0.30/0.46 ( ( ( secrecy_sE @ X22 )
% 0.30/0.46 = ( secrecy_sE @ Y22 ) )
% 0.30/0.46 = ( X22 = Y22 ) ) ).
% 0.30/0.46
% 0.30/0.46 % Expression.inject(2)
% 0.30/0.46 thf(fact_111_Un__empty,axiom,
% 0.30/0.46 ! [A: $tType,A3: set @ A,B: set @ A] :
% 0.30/0.46 ( ( ( sup_sup @ ( set @ A ) @ A3 @ B )
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 = ( ( A3
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 & ( B
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_empty
% 0.30/0.46 thf(fact_112_Un__insert__right,axiom,
% 0.30/0.46 ! [A: $tType,A3: set @ A,A2: A,B: set @ A] :
% 0.30/0.46 ( ( sup_sup @ ( set @ A ) @ A3 @ ( insert @ A @ A2 @ B ) )
% 0.30/0.46 = ( insert @ A @ A2 @ ( sup_sup @ ( set @ A ) @ A3 @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_insert_right
% 0.30/0.46 thf(fact_113_Un__insert__left,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,B: set @ A,C4: set @ A] :
% 0.30/0.46 ( ( sup_sup @ ( set @ A ) @ ( insert @ A @ A2 @ B ) @ C4 )
% 0.30/0.46 = ( insert @ A @ A2 @ ( sup_sup @ ( set @ A ) @ B @ C4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_insert_left
% 0.30/0.46 thf(fact_114_UnE,axiom,
% 0.30/0.46 ! [A: $tType,C: A,A3: set @ A,B: set @ A] :
% 0.30/0.46 ( ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A3 @ B ) )
% 0.30/0.46 => ( ~ ( member @ A @ C @ A3 )
% 0.30/0.46 => ( member @ A @ C @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % UnE
% 0.30/0.46 thf(fact_115_UnI1,axiom,
% 0.30/0.46 ! [A: $tType,C: A,A3: set @ A,B: set @ A] :
% 0.30/0.46 ( ( member @ A @ C @ A3 )
% 0.30/0.46 => ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A3 @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % UnI1
% 0.30/0.46 thf(fact_116_UnI2,axiom,
% 0.30/0.46 ! [A: $tType,C: A,B: set @ A,A3: set @ A] :
% 0.30/0.46 ( ( member @ A @ C @ B )
% 0.30/0.46 => ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A3 @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % UnI2
% 0.30/0.46 thf(fact_117_bex__Un,axiom,
% 0.30/0.46 ! [A: $tType,A3: set @ A,B: set @ A,P: A > $o] :
% 0.30/0.46 ( ( ? [X2: A] :
% 0.30/0.46 ( ( member @ A @ X2 @ ( sup_sup @ ( set @ A ) @ A3 @ B ) )
% 0.30/0.46 & ( P @ X2 ) ) )
% 0.30/0.46 = ( ? [X2: A] :
% 0.30/0.46 ( ( member @ A @ X2 @ A3 )
% 0.30/0.46 & ( P @ X2 ) )
% 0.30/0.46 | ? [X2: A] :
% 0.30/0.46 ( ( member @ A @ X2 @ B )
% 0.30/0.46 & ( P @ X2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bex_Un
% 0.30/0.46 thf(fact_118_ball__Un,axiom,
% 0.30/0.46 ! [A: $tType,A3: set @ A,B: set @ A,P: A > $o] :
% 0.30/0.46 ( ( ! [X2: A] :
% 0.30/0.46 ( ( member @ A @ X2 @ ( sup_sup @ ( set @ A ) @ A3 @ B ) )
% 0.30/0.46 => ( P @ X2 ) ) )
% 0.30/0.46 = ( ! [X2: A] :
% 0.30/0.46 ( ( member @ A @ X2 @ A3 )
% 0.30/0.46 => ( P @ X2 ) )
% 0.30/0.46 & ! [X2: A] :
% 0.30/0.46 ( ( member @ A @ X2 @ B )
% 0.30/0.46 => ( P @ X2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ball_Un
% 0.30/0.46 thf(fact_119_Un__assoc,axiom,
% 0.30/0.46 ! [A: $tType,A3: set @ A,B: set @ A,C4: set @ A] :
% 0.30/0.46 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A3 @ B ) @ C4 )
% 0.30/0.46 = ( sup_sup @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ B @ C4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_assoc
% 0.30/0.46 thf(fact_120_Un__absorb,axiom,
% 0.30/0.46 ! [A: $tType,A3: set @ A] :
% 0.30/0.46 ( ( sup_sup @ ( set @ A ) @ A3 @ A3 )
% 0.30/0.46 = A3 ) ).
% 0.30/0.46
% 0.30/0.46 % Un_absorb
% 0.30/0.46 thf(fact_121_Un__commute,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( sup_sup @ ( set @ A ) )
% 0.30/0.46 = ( ^ [A4: set @ A,B5: set @ A] : ( sup_sup @ ( set @ A ) @ B5 @ A4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_commute
% 0.30/0.46 thf(fact_122_Un__left__absorb,axiom,
% 0.30/0.46 ! [A: $tType,A3: set @ A,B: set @ A] :
% 0.30/0.46 ( ( sup_sup @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ A3 @ B ) )
% 0.30/0.46 = ( sup_sup @ ( set @ A ) @ A3 @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_left_absorb
% 0.30/0.46 thf(fact_123_Un__left__commute,axiom,
% 0.30/0.46 ! [A: $tType,A3: set @ A,B: set @ A,C4: set @ A] :
% 0.30/0.46 ( ( sup_sup @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ B @ C4 ) )
% 0.30/0.46 = ( sup_sup @ ( set @ A ) @ B @ ( sup_sup @ ( set @ A ) @ A3 @ C4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_left_commute
% 0.30/0.46 thf(fact_124_KS2Expression_Osimps_I2_J,axiom,
% 0.30/0.46 ! [M2: secrecy_Secrets] :
% 0.30/0.46 ( ( secrec1016742679ession @ ( secrecy_sKS @ M2 ) )
% 0.30/0.46 = ( secrecy_sE @ M2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % KS2Expression.simps(2)
% 0.30/0.46 thf(fact_125_Un__empty__right,axiom,
% 0.30/0.46 ! [A: $tType,A3: set @ A] :
% 0.30/0.46 ( ( sup_sup @ ( set @ A ) @ A3 @ ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 = A3 ) ).
% 0.30/0.46
% 0.30/0.46 % Un_empty_right
% 0.30/0.46 thf(fact_126_Un__empty__left,axiom,
% 0.30/0.46 ! [A: $tType,B: set @ A] :
% 0.30/0.46 ( ( sup_sup @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ B )
% 0.30/0.46 = B ) ).
% 0.30/0.46
% 0.30/0.46 % Un_empty_left
% 0.30/0.46 thf(fact_127_not__know__s__not__ine,axiom,
% 0.30/0.46 ! [A3: secrecy_specID,M2: secrecy_Secrets] :
% 0.30/0.46 ( ~ ( knowle1437066798e_know @ A3 @ ( secrecy_sKS @ M2 ) )
% 0.30/0.46 => ~ ( ine @ A3 @ ( secrecy_sE @ M2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % not_know_s_not_ine
% 0.30/0.46 thf(fact_128_KS_Oexhaust,axiom,
% 0.30/0.46 ! [Y2: secrecy_KS] :
% 0.30/0.46 ( ! [X12: secrecy_Keys] :
% 0.30/0.46 ( Y2
% 0.30/0.46 != ( secrecy_kKS @ X12 ) )
% 0.30/0.46 => ~ ! [X23: secrecy_Secrets] :
% 0.30/0.46 ( Y2
% 0.30/0.46 != ( secrecy_sKS @ X23 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % KS.exhaust
% 0.30/0.46 thf(fact_129_KS_Oinduct,axiom,
% 0.30/0.46 ! [P: secrecy_KS > $o,KS: secrecy_KS] :
% 0.30/0.46 ( ! [X3: secrecy_Keys] : ( P @ ( secrecy_kKS @ X3 ) )
% 0.30/0.46 => ( ! [X3: secrecy_Secrets] : ( P @ ( secrecy_sKS @ X3 ) )
% 0.30/0.46 => ( P @ KS ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % KS.induct
% 0.30/0.46 thf(fact_130_KS_Odistinct_I1_J,axiom,
% 0.30/0.46 ! [X1: secrecy_Keys,X22: secrecy_Secrets] :
% 0.30/0.46 ( ( secrecy_kKS @ X1 )
% 0.30/0.46 != ( secrecy_sKS @ X22 ) ) ).
% 0.30/0.46
% 0.30/0.46 % KS.distinct(1)
% 0.30/0.46 thf(fact_131_Expression_Odistinct_I1_J,axiom,
% 0.30/0.46 ! [X1: secrecy_Keys,X22: secrecy_Secrets] :
% 0.30/0.46 ( ( secrecy_kE @ X1 )
% 0.30/0.46 != ( secrecy_sE @ X22 ) ) ).
% 0.30/0.46
% 0.30/0.46 % Expression.distinct(1)
% 0.30/0.46 thf(fact_132_know_Osimps_I2_J,axiom,
% 0.30/0.46 ! [A3: secrecy_specID,M2: secrecy_Secrets] :
% 0.30/0.46 ( ( knowle1437066798e_know @ A3 @ ( secrecy_sKS @ M2 ) )
% 0.30/0.46 = ( ( ine @ A3 @ ( secrecy_sE @ M2 ) )
% 0.30/0.46 | ( member @ secrecy_KS @ ( secrecy_sKS @ M2 ) @ ( localSecrets @ A3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % know.simps(2)
% 0.30/0.46 thf(fact_133_singleton__Un__iff,axiom,
% 0.30/0.46 ! [A: $tType,X: A,A3: set @ A,B: set @ A] :
% 0.30/0.46 ( ( ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 = ( sup_sup @ ( set @ A ) @ A3 @ B ) )
% 0.30/0.46 = ( ( ( A3
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 & ( B
% 0.30/0.46 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.30/0.46 | ( ( A3
% 0.30/0.46 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.46 & ( B
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.46 | ( ( A3
% 0.30/0.46 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.46 & ( B
% 0.30/0.46 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % singleton_Un_iff
% 0.30/0.46 thf(fact_134_Un__singleton__iff,axiom,
% 0.30/0.46 ! [A: $tType,A3: set @ A,B: set @ A,X: A] :
% 0.30/0.46 ( ( ( sup_sup @ ( set @ A ) @ A3 @ B )
% 0.30/0.46 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.46 = ( ( ( A3
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 & ( B
% 0.30/0.46 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.30/0.46 | ( ( A3
% 0.30/0.46 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.46 & ( B
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.46 | ( ( A3
% 0.30/0.46 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.46 & ( B
% 0.30/0.46 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_singleton_iff
% 0.30/0.46 thf(fact_135_insert__is__Un,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( insert @ A )
% 0.30/0.46 = ( ^ [A5: A] : ( sup_sup @ ( set @ A ) @ ( insert @ A @ A5 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_is_Un
% 0.30/0.46 thf(fact_136_LocalSecretsComposition__neg__loc__s,axiom,
% 0.30/0.46 ! [Secret: secrecy_Secrets,P: secrecy_specID,Ch: secrecy_chanID] :
% 0.30/0.46 ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ P ) )
% 0.30/0.46 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 0.30/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ P ) )
% 0.30/0.46 => ~ ( member @ secrecy_chanID @ Ch @ ( loc @ P ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % LocalSecretsComposition_neg_loc_s
% 0.30/0.46 thf(fact_137_LocalSecretsComposition__neg__s,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,M2: secrecy_Secrets] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correc965049635ionLoc @ PQ )
% 0.30/0.46 => ( ( correctCompositionKS @ PQ )
% 0.30/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ M2 ) @ ( specKeysSecrets @ P ) )
% 0.30/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ M2 ) @ ( specKeysSecrets @ Q ) )
% 0.30/0.46 => ( ~ ( ine @ P @ ( secrecy_sE @ M2 ) )
% 0.30/0.46 => ( ~ ( ine @ Q @ ( secrecy_sE @ M2 ) )
% 0.30/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ M2 ) @ ( sup_sup @ ( set @ secrecy_KS ) @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 0.30/0.46 => ~ ( member @ secrecy_KS @ ( secrecy_sKS @ M2 ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % LocalSecretsComposition_neg_s
% 0.30/0.46 thf(fact_138_LocalSecretsComposition__ine1__s,axiom,
% 0.30/0.46 ! [S: secrecy_Secrets,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 0.30/0.46 ( ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correc965049635ionLoc @ PQ )
% 0.30/0.46 => ( ~ ( ine @ Q @ ( secrecy_sE @ S ) )
% 0.30/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 0.30/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 0.30/0.46 => ( ine @ P @ ( secrecy_sE @ S ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % LocalSecretsComposition_ine1_s
% 0.30/0.46 thf(fact_139_LocalSecretsComposition__ine2__s,axiom,
% 0.30/0.46 ! [S: secrecy_Secrets,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 0.30/0.46 ( ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correc965049635ionLoc @ PQ )
% 0.30/0.46 => ( ~ ( ine @ P @ ( secrecy_sE @ S ) )
% 0.30/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 0.30/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 0.30/0.46 => ( ine @ Q @ ( secrecy_sE @ S ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % LocalSecretsComposition_ine2_s
% 0.30/0.46 thf(fact_140_LocalSecretsComposition__neg1__s,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,S: secrecy_Secrets] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correc965049635ionLoc @ PQ )
% 0.30/0.46 => ( ~ ( ine @ P @ ( secrecy_sE @ S ) )
% 0.30/0.46 => ( ~ ( ine @ Q @ ( secrecy_sE @ S ) )
% 0.30/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 0.30/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 0.30/0.46 => ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % LocalSecretsComposition_neg1_s
% 0.30/0.46 thf(fact_141_LocalSecretsComposition__exprChannel__s,axiom,
% 0.30/0.46 ! [X: secrecy_chanID,Secrets: secrecy_Secrets,P: secrecy_specID,Q: secrecy_specID] :
% 0.30/0.46 ( ( exprChannel @ X @ ( secrecy_sE @ Secrets ) )
% 0.30/0.46 => ( ~ ( ine @ P @ ( secrecy_sE @ Secrets ) )
% 0.30/0.46 => ( ~ ( ine @ Q @ ( secrecy_sE @ Secrets ) )
% 0.30/0.46 => ( ~ ( member @ secrecy_chanID @ X @ ( ins @ P ) )
% 0.30/0.46 & ~ ( member @ secrecy_chanID @ X @ ( ins @ Q ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % LocalSecretsComposition_exprChannel_s
% 0.30/0.46 thf(fact_142_LocalSecretsComposition__neg,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correc965049635ionLoc @ PQ )
% 0.30/0.46 => ( ( correctCompositionKS @ PQ )
% 0.30/0.46 => ( ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 0.30/0.46 => ( ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) )
% 0.30/0.46 => ( ! [M4: secrecy_Keys] :
% 0.30/0.46 ( ( Ks
% 0.30/0.46 = ( secrecy_kKS @ M4 ) )
% 0.30/0.46 => ( ~ ( ine @ P @ ( secrecy_kE @ M4 ) )
% 0.30/0.46 & ~ ( ine @ Q @ ( secrecy_kE @ M4 ) ) ) )
% 0.30/0.46 => ( ! [M4: secrecy_Secrets] :
% 0.30/0.46 ( ( Ks
% 0.30/0.46 = ( secrecy_sKS @ M4 ) )
% 0.30/0.46 => ( ~ ( ine @ P @ ( secrecy_sE @ M4 ) )
% 0.30/0.46 & ~ ( ine @ Q @ ( secrecy_sE @ M4 ) ) ) )
% 0.30/0.46 => ( ~ ( member @ secrecy_KS @ Ks @ ( sup_sup @ ( set @ secrecy_KS ) @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 0.30/0.46 => ~ ( member @ secrecy_KS @ Ks @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % LocalSecretsComposition_neg
% 0.30/0.46 thf(fact_143_LocalSecretsComposition__neg1,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correc965049635ionLoc @ PQ )
% 0.30/0.46 => ( ! [M4: secrecy_Keys] :
% 0.30/0.46 ( ( Ks
% 0.30/0.46 = ( secrecy_kKS @ M4 ) )
% 0.30/0.46 => ( ~ ( ine @ P @ ( secrecy_kE @ M4 ) )
% 0.30/0.46 & ~ ( ine @ Q @ ( secrecy_kE @ M4 ) ) ) )
% 0.30/0.46 => ( ! [M4: secrecy_Secrets] :
% 0.30/0.46 ( ( Ks
% 0.30/0.46 = ( secrecy_sKS @ M4 ) )
% 0.30/0.46 => ( ~ ( ine @ P @ ( secrecy_sE @ M4 ) )
% 0.30/0.46 & ~ ( ine @ Q @ ( secrecy_sE @ M4 ) ) ) )
% 0.30/0.46 => ( ~ ( member @ secrecy_KS @ Ks @ ( localSecrets @ P ) )
% 0.30/0.46 => ( ~ ( member @ secrecy_KS @ Ks @ ( localSecrets @ Q ) )
% 0.30/0.46 => ~ ( member @ secrecy_KS @ Ks @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % LocalSecretsComposition_neg1
% 0.30/0.46 thf(fact_144_correctCompositionKS__exprChannel__s__Qex,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correctCompositionKS @ PQ )
% 0.30/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 0.30/0.46 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ Q ) )
% 0.30/0.46 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 0.30/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 0.30/0.46 => ( ( correctCompositionIn @ PQ )
% 0.30/0.46 => ? [Ch4: secrecy_chanID] :
% 0.30/0.46 ( ( member @ secrecy_chanID @ Ch4 @ ( ins @ PQ ) )
% 0.30/0.46 & ( exprChannel @ Ch4 @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % correctCompositionKS_exprChannel_s_Qex
% 0.30/0.46 thf(fact_145_sup__bot_Oright__neutral,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( bounde1808546759up_bot @ A )
% 0.30/0.46 => ! [A2: A] :
% 0.30/0.46 ( ( sup_sup @ A @ A2 @ ( bot_bot @ A ) )
% 0.30/0.46 = A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup_bot.right_neutral
% 0.30/0.46 thf(fact_146_sup__bot_Oneutr__eq__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( bounde1808546759up_bot @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( ( bot_bot @ A )
% 0.30/0.46 = ( sup_sup @ A @ A2 @ B2 ) )
% 0.30/0.46 = ( ( A2
% 0.30/0.46 = ( bot_bot @ A ) )
% 0.30/0.46 & ( B2
% 0.30/0.46 = ( bot_bot @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup_bot.neutr_eq_iff
% 0.30/0.46 thf(fact_147_sup__bot_Oleft__neutral,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( bounde1808546759up_bot @ A )
% 0.30/0.46 => ! [A2: A] :
% 0.30/0.46 ( ( sup_sup @ A @ ( bot_bot @ A ) @ A2 )
% 0.30/0.46 = A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup_bot.left_neutral
% 0.30/0.46 thf(fact_148_sup__bot_Oeq__neutr__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( bounde1808546759up_bot @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( ( sup_sup @ A @ A2 @ B2 )
% 0.30/0.46 = ( bot_bot @ A ) )
% 0.30/0.46 = ( ( A2
% 0.30/0.46 = ( bot_bot @ A ) )
% 0.30/0.46 & ( B2
% 0.30/0.46 = ( bot_bot @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup_bot.eq_neutr_iff
% 0.30/0.46 thf(fact_149_sup__eq__bot__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( bounde1808546759up_bot @ A )
% 0.30/0.46 => ! [X: A,Y2: A] :
% 0.30/0.46 ( ( ( sup_sup @ A @ X @ Y2 )
% 0.30/0.46 = ( bot_bot @ A ) )
% 0.30/0.46 = ( ( X
% 0.30/0.46 = ( bot_bot @ A ) )
% 0.30/0.46 & ( Y2
% 0.30/0.46 = ( bot_bot @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup_eq_bot_iff
% 0.30/0.46 thf(fact_150_sup__bot__left,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( bounde1808546759up_bot @ A )
% 0.30/0.46 => ! [X: A] :
% 0.30/0.46 ( ( sup_sup @ A @ ( bot_bot @ A ) @ X )
% 0.30/0.46 = X ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup_bot_left
% 0.30/0.46 thf(fact_151_sup__bot__right,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( bounde1808546759up_bot @ A )
% 0.30/0.46 => ! [X: A] :
% 0.30/0.46 ( ( sup_sup @ A @ X @ ( bot_bot @ A ) )
% 0.30/0.46 = X ) ) ).
% 0.30/0.46
% 0.30/0.46 % sup_bot_right
% 0.30/0.46 thf(fact_152_bot__eq__sup__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( bounde1808546759up_bot @ A )
% 0.30/0.46 => ! [X: A,Y2: A] :
% 0.30/0.46 ( ( ( bot_bot @ A )
% 0.30/0.46 = ( sup_sup @ A @ X @ Y2 ) )
% 0.30/0.46 = ( ( X
% 0.30/0.46 = ( bot_bot @ A ) )
% 0.30/0.46 & ( Y2
% 0.30/0.46 = ( bot_bot @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot_eq_sup_iff
% 0.30/0.46 thf(fact_153_ineM__Un1,axiom,
% 0.30/0.46 ! [P: secrecy_specID,A3: set @ secrecy_chanID,E: secrecy_Expression,B: set @ secrecy_chanID] :
% 0.30/0.46 ( ( ineM @ P @ A3 @ E )
% 0.30/0.46 => ( ineM @ P @ ( sup_sup @ ( set @ secrecy_chanID ) @ A3 @ B ) @ E ) ) ).
% 0.30/0.46
% 0.30/0.46 % ineM_Un1
% 0.30/0.46 thf(fact_154_locStream__def,axiom,
% 0.30/0.46 ( locStream
% 0.30/0.46 = ( ^ [X2: secrecy_specID] :
% 0.30/0.46 ( ^ [Y3: set @ secrecy_chanID,Z: set @ secrecy_chanID] : ( Y3 = Z )
% 0.30/0.46 @ ( loc @ X2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % locStream_def
% 0.30/0.46 thf(fact_155_inStream__def,axiom,
% 0.30/0.46 ( inStream
% 0.30/0.46 = ( ^ [X2: secrecy_specID] :
% 0.30/0.46 ( ^ [Y3: set @ secrecy_chanID,Z: set @ secrecy_chanID] : ( Y3 = Z )
% 0.30/0.46 @ ( ins @ X2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inStream_def
% 0.30/0.46 thf(fact_156_notSpecKeysSecretsExpr__def,axiom,
% 0.30/0.46 ( notSpe1586871396tsExpr
% 0.30/0.46 = ( ^ [P2: secrecy_specID,E3: list @ secrecy_Expression] :
% 0.30/0.46 ( ! [X2: secrecy_Keys] :
% 0.30/0.46 ( ( mem @ secrecy_Expression @ ( secrecy_kE @ X2 ) @ E3 )
% 0.30/0.46 => ~ ( member @ secrecy_KS @ ( secrecy_kKS @ X2 ) @ ( specKeysSecrets @ P2 ) ) )
% 0.30/0.46 & ! [Y4: secrecy_Secrets] :
% 0.30/0.46 ( ( mem @ secrecy_Expression @ ( secrecy_sE @ Y4 ) @ E3 )
% 0.30/0.46 => ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Y4 ) @ ( specKeysSecrets @ P2 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % notSpecKeysSecretsExpr_def
% 0.30/0.46 thf(fact_157_TBtheorem5a__empty,axiom,
% 0.30/0.46 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.30/0.46 ( ( ( eout @ P @ E )
% 0.30/0.46 | ( eout @ Q @ E ) )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.30/0.46 => ( ( ( loc @ PQ )
% 0.30/0.46 = ( bot_bot @ ( set @ secrecy_chanID ) ) )
% 0.30/0.46 => ( eout @ PQ @ E ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem5a_empty
% 0.30/0.46 thf(fact_158_correctCompositionKS__subcomp4,axiom,
% 0.30/0.46 ! [C4: secrecy_specID,X: secrecy_specID,Xa: secrecy_Secrets] :
% 0.30/0.46 ( ( correctCompositionKS @ C4 )
% 0.30/0.46 => ( ( member @ secrecy_specID @ X @ ( subcomponents @ C4 ) )
% 0.30/0.46 => ( ( member @ secrecy_Secrets @ Xa @ ( specSecrets @ X ) )
% 0.30/0.46 => ( member @ secrecy_Secrets @ Xa @ ( specSecrets @ C4 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % correctCompositionKS_subcomp4
% 0.30/0.46 thf(fact_159_correctCompositionKS__subcomp3,axiom,
% 0.30/0.46 ! [C4: secrecy_specID,X: secrecy_specID,Xa: secrecy_Keys] :
% 0.30/0.46 ( ( correctCompositionKS @ C4 )
% 0.30/0.46 => ( ( member @ secrecy_specID @ X @ ( subcomponents @ C4 ) )
% 0.30/0.46 => ( ( member @ secrecy_Keys @ Xa @ ( specKeys @ X ) )
% 0.30/0.46 => ( member @ secrecy_Keys @ Xa @ ( specKeys @ C4 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % correctCompositionKS_subcomp3
% 0.30/0.46 thf(fact_160_TBtheorem2a,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.30/0.46 ( ( eout @ PQ @ E )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.30/0.46 => ( ( eout @ P @ E )
% 0.30/0.46 | ( eout @ Q @ E ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem2a
% 0.30/0.46 thf(fact_161_correctCompositionKS__subcomp1,axiom,
% 0.30/0.46 ! [C4: secrecy_specID,X: secrecy_specID,Xa: secrecy_Keys] :
% 0.30/0.46 ( ( correctCompositionKS @ C4 )
% 0.30/0.46 => ( ( member @ secrecy_specID @ X @ ( subcomponents @ C4 ) )
% 0.30/0.46 => ( ( member @ secrecy_Keys @ Xa @ ( specKeys @ C4 ) )
% 0.30/0.46 => ? [X3: secrecy_specID] :
% 0.30/0.46 ( ( member @ secrecy_specID @ X3 @ ( subcomponents @ C4 ) )
% 0.30/0.46 & ( member @ secrecy_Keys @ Xa @ ( specKeys @ X3 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % correctCompositionKS_subcomp1
% 0.30/0.46 thf(fact_162_correctCompositionKS__subcomp2,axiom,
% 0.30/0.46 ! [C4: secrecy_specID,X: secrecy_specID,Xa: secrecy_Secrets] :
% 0.30/0.46 ( ( correctCompositionKS @ C4 )
% 0.30/0.46 => ( ( member @ secrecy_specID @ X @ ( subcomponents @ C4 ) )
% 0.30/0.46 => ( ( member @ secrecy_Secrets @ Xa @ ( specSecrets @ C4 ) )
% 0.30/0.46 => ? [X3: secrecy_specID] :
% 0.30/0.46 ( ( member @ secrecy_specID @ X3 @ ( subcomponents @ C4 ) )
% 0.30/0.46 & ( member @ secrecy_Secrets @ Xa @ ( specSecrets @ X3 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % correctCompositionKS_subcomp2
% 0.30/0.46 thf(fact_163_TBtheorem5a__notP1,axiom,
% 0.30/0.46 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.30/0.46 ( ( eout @ P @ E )
% 0.30/0.46 => ( ~ ( eout @ Q @ E )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.30/0.46 => ( ? [Ch3: secrecy_chanID] :
% 0.30/0.46 ( ( out_ex985543062Single @ P @ Ch3 @ E )
% 0.30/0.46 & ( member @ secrecy_chanID @ Ch3 @ ( loc @ PQ ) ) )
% 0.30/0.46 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem5a_notP1
% 0.30/0.46 thf(fact_164_TBtheorem5a__notP2,axiom,
% 0.30/0.46 ! [Q: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set @ secrecy_chanID] :
% 0.30/0.46 ( ~ ( eout @ Q @ E )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.30/0.46 => ( ( out_exprChannelSet @ P @ ChSet @ E )
% 0.30/0.46 => ( ! [X3: secrecy_chanID] :
% 0.30/0.46 ( ( member @ secrecy_chanID @ X3 @ ChSet )
% 0.30/0.46 => ( member @ secrecy_chanID @ X3 @ ( loc @ PQ ) ) )
% 0.30/0.46 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem5a_notP2
% 0.30/0.46 thf(fact_165_TBtheorem5a__notPQ,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set @ secrecy_chanID,E: secrecy_Expression,ChSetQ: set @ secrecy_chanID] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.30/0.46 => ( ( out_exprChannelSet @ P @ ChSetP @ E )
% 0.30/0.46 => ( ( out_exprChannelSet @ Q @ ChSetQ @ E )
% 0.30/0.46 => ( ! [X3: secrecy_chanID] :
% 0.30/0.46 ( ( member @ secrecy_chanID @ X3 @ ChSetP )
% 0.30/0.46 => ( member @ secrecy_chanID @ X3 @ ( loc @ PQ ) ) )
% 0.30/0.46 => ( ! [X3: secrecy_chanID] :
% 0.30/0.46 ( ( member @ secrecy_chanID @ X3 @ ChSetQ )
% 0.30/0.46 => ( member @ secrecy_chanID @ X3 @ ( loc @ PQ ) ) )
% 0.30/0.46 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem5a_notPQ
% 0.30/0.46 thf(fact_166_out__exprChannelSet__Single,axiom,
% 0.30/0.46 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 0.30/0.46 ( ( out_exprChannelSet @ P @ ( insert @ secrecy_chanID @ Ch @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ E )
% 0.30/0.46 => ( out_ex985543062Single @ P @ Ch @ E ) ) ).
% 0.30/0.46
% 0.30/0.46 % out_exprChannelSet_Single
% 0.30/0.46 thf(fact_167_out__exprChannelSingle__Set,axiom,
% 0.30/0.46 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 0.30/0.46 ( ( out_ex985543062Single @ P @ Ch @ E )
% 0.30/0.46 => ( out_exprChannelSet @ P @ ( insert @ secrecy_chanID @ Ch @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ E ) ) ).
% 0.30/0.46
% 0.30/0.46 % out_exprChannelSingle_Set
% 0.30/0.46 thf(fact_168_TBtheorem5b__notPQ,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set @ secrecy_chanID,E: secrecy_Expression,ChSetQ: set @ secrecy_chanID,M: set @ secrecy_chanID] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.30/0.46 => ( ( out_exprChannelSet @ P @ ChSetP @ E )
% 0.30/0.46 => ( ( out_exprChannelSet @ Q @ ChSetQ @ E )
% 0.30/0.46 => ( ( M
% 0.30/0.46 = ( sup_sup @ ( set @ secrecy_chanID ) @ ChSetP @ ChSetQ ) )
% 0.30/0.46 => ( ! [X3: secrecy_chanID] :
% 0.30/0.46 ( ( member @ secrecy_chanID @ X3 @ ChSetP )
% 0.30/0.46 => ( member @ secrecy_chanID @ X3 @ ( loc @ PQ ) ) )
% 0.30/0.46 => ( ! [X3: secrecy_chanID] :
% 0.30/0.46 ( ( member @ secrecy_chanID @ X3 @ ChSetQ )
% 0.30/0.46 => ( member @ secrecy_chanID @ X3 @ ( loc @ PQ ) ) )
% 0.30/0.46 => ~ ( eoutM @ PQ @ M @ E ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem5b_notPQ
% 0.30/0.46 thf(fact_169_eout__know__s,axiom,
% 0.30/0.46 ! [C4: secrecy_specID,M2: secrecy_Secrets] :
% 0.30/0.46 ( ( knowle1667810483orrect @ C4 @ ( secrecy_sKS @ M2 ) )
% 0.30/0.46 = ( ( eout @ C4 @ ( secrecy_sE @ M2 ) )
% 0.30/0.46 = ( ( member @ secrecy_Secrets @ M2 @ ( specSecrets @ C4 ) )
% 0.30/0.46 | ( knowle1437066798e_know @ C4 @ ( secrecy_sKS @ M2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eout_know_s
% 0.30/0.46 thf(fact_170_not__know__s__not__eout,axiom,
% 0.30/0.46 ! [M2: secrecy_Secrets,A3: secrecy_specID] :
% 0.30/0.46 ( ~ ( member @ secrecy_Secrets @ M2 @ ( specSecrets @ A3 ) )
% 0.30/0.46 => ( ~ ( knowle1437066798e_know @ A3 @ ( secrecy_sKS @ M2 ) )
% 0.30/0.46 => ( ( knowle1667810483orrect @ A3 @ ( secrecy_sKS @ M2 ) )
% 0.30/0.46 => ~ ( eout @ A3 @ ( secrecy_sE @ M2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % not_know_s_not_eout
% 0.30/0.46 thf(fact_171_not__eout__eoutM,axiom,
% 0.30/0.46 ! [P: secrecy_specID,E: secrecy_Expression,M: set @ secrecy_chanID] :
% 0.30/0.46 ( ~ ( eout @ P @ E )
% 0.30/0.46 => ~ ( eoutM @ P @ M @ E ) ) ).
% 0.30/0.46
% 0.30/0.46 % not_eout_eoutM
% 0.30/0.46 thf(fact_172_eoutM__eout,axiom,
% 0.30/0.46 ! [P: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression] :
% 0.30/0.46 ( ( eoutM @ P @ M @ E )
% 0.30/0.46 => ( eout @ P @ E ) ) ).
% 0.30/0.46
% 0.30/0.46 % eoutM_eout
% 0.30/0.46 thf(fact_173_TBtheorem2b,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.30/0.46 ( ( eoutM @ PQ @ M @ E )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.30/0.46 => ( ( eoutM @ P @ M @ E )
% 0.30/0.46 | ( eoutM @ Q @ M @ E ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem2b
% 0.30/0.46 thf(fact_174_TBtheorem5b__notP2,axiom,
% 0.30/0.46 ! [Q: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set @ secrecy_chanID] :
% 0.30/0.46 ( ~ ( eoutM @ Q @ M @ E )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.30/0.46 => ( ( out_exprChannelSet @ P @ ChSet @ E )
% 0.30/0.46 => ( ! [X3: secrecy_chanID] :
% 0.30/0.46 ( ( member @ secrecy_chanID @ X3 @ ChSet )
% 0.30/0.46 => ( member @ secrecy_chanID @ X3 @ ( loc @ PQ ) ) )
% 0.30/0.46 => ~ ( eoutM @ PQ @ M @ E ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem5b_notP2
% 0.30/0.46 thf(fact_175_TBtheorem5b__notP1,axiom,
% 0.30/0.46 ! [P: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.30/0.46 ( ( eoutM @ P @ M @ E )
% 0.30/0.46 => ( ~ ( eoutM @ Q @ M @ E )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.30/0.46 => ( ? [Ch3: secrecy_chanID] :
% 0.30/0.46 ( ( out_ex985543062Single @ P @ Ch3 @ E )
% 0.30/0.46 & ( member @ secrecy_chanID @ Ch3 @ M )
% 0.30/0.46 & ( member @ secrecy_chanID @ Ch3 @ ( loc @ PQ ) ) )
% 0.30/0.46 => ~ ( eoutM @ PQ @ M @ E ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem5b_notP1
% 0.30/0.46 thf(fact_176_eout__know__k,axiom,
% 0.30/0.46 ! [C4: secrecy_specID,M2: secrecy_Keys] :
% 0.30/0.46 ( ( knowle1667810483orrect @ C4 @ ( secrecy_kKS @ M2 ) )
% 0.30/0.46 = ( ( eout @ C4 @ ( secrecy_kE @ M2 ) )
% 0.30/0.46 = ( ( member @ secrecy_Keys @ M2 @ ( specKeys @ C4 ) )
% 0.30/0.46 | ( knowle1437066798e_know @ C4 @ ( secrecy_kKS @ M2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eout_know_k
% 0.30/0.46 thf(fact_177_not__know__k__not__eout,axiom,
% 0.30/0.46 ! [M2: secrecy_Keys,A3: secrecy_specID] :
% 0.30/0.46 ( ~ ( member @ secrecy_Keys @ M2 @ ( specKeys @ A3 ) )
% 0.30/0.46 => ( ~ ( knowle1437066798e_know @ A3 @ ( secrecy_kKS @ M2 ) )
% 0.30/0.46 => ( ( knowle1667810483orrect @ A3 @ ( secrecy_kKS @ M2 ) )
% 0.30/0.46 => ~ ( eout @ A3 @ ( secrecy_kE @ M2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % not_know_k_not_eout
% 0.30/0.46 thf(fact_178_eoutKnowCorrect__L1k,axiom,
% 0.30/0.46 ! [C4: secrecy_specID,M2: secrecy_Keys] :
% 0.30/0.46 ( ( knowle1667810483orrect @ C4 @ ( secrecy_kKS @ M2 ) )
% 0.30/0.46 => ( ( eout @ C4 @ ( secrecy_kE @ M2 ) )
% 0.30/0.46 => ( ( member @ secrecy_Keys @ M2 @ ( specKeys @ C4 ) )
% 0.30/0.46 | ( knowle1437066798e_know @ C4 @ ( secrecy_kKS @ M2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eoutKnowCorrect_L1k
% 0.30/0.46 thf(fact_179_eout__know__nonKS__k,axiom,
% 0.30/0.46 ! [M2: secrecy_Keys,A3: secrecy_specID] :
% 0.30/0.46 ( ~ ( member @ secrecy_Keys @ M2 @ ( specKeys @ A3 ) )
% 0.30/0.46 => ( ( eout @ A3 @ ( secrecy_kE @ M2 ) )
% 0.30/0.46 => ( ( knowle1667810483orrect @ A3 @ ( secrecy_kKS @ M2 ) )
% 0.30/0.46 => ( knowle1437066798e_know @ A3 @ ( secrecy_kKS @ M2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eout_know_nonKS_k
% 0.30/0.46 thf(fact_180_eout__know__nonKS__s,axiom,
% 0.30/0.46 ! [M2: secrecy_Secrets,A3: secrecy_specID] :
% 0.30/0.46 ( ~ ( member @ secrecy_Secrets @ M2 @ ( specSecrets @ A3 ) )
% 0.30/0.46 => ( ( eout @ A3 @ ( secrecy_sE @ M2 ) )
% 0.30/0.46 => ( ( knowle1667810483orrect @ A3 @ ( secrecy_sKS @ M2 ) )
% 0.30/0.46 => ( knowle1437066798e_know @ A3 @ ( secrecy_sKS @ M2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eout_know_nonKS_s
% 0.30/0.46 thf(fact_181_eoutKnowCorrect__L1s,axiom,
% 0.30/0.46 ! [C4: secrecy_specID,M2: secrecy_Secrets] :
% 0.30/0.46 ( ( knowle1667810483orrect @ C4 @ ( secrecy_sKS @ M2 ) )
% 0.30/0.46 => ( ( eout @ C4 @ ( secrecy_sE @ M2 ) )
% 0.30/0.46 => ( ( member @ secrecy_Secrets @ M2 @ ( specSecrets @ C4 ) )
% 0.30/0.46 | ( knowle1437066798e_know @ C4 @ ( secrecy_sKS @ M2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eoutKnowCorrect_L1s
% 0.30/0.46 thf(fact_182_TBtheorem5b__PQ,axiom,
% 0.30/0.46 ! [P: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.30/0.46 ( ( ( eoutM @ P @ M @ E )
% 0.30/0.46 | ( eoutM @ Q @ M @ E ) )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.30/0.46 => ( ? [Ch3: secrecy_chanID] :
% 0.30/0.46 ( ( ( member @ secrecy_chanID @ Ch3 @ ( out @ P ) )
% 0.30/0.46 | ( member @ secrecy_chanID @ Ch3 @ ( out @ Q ) ) )
% 0.30/0.46 & ( member @ secrecy_chanID @ Ch3 @ M )
% 0.30/0.46 & ( exprChannel @ Ch3 @ E )
% 0.30/0.46 & ~ ( member @ secrecy_chanID @ Ch3 @ ( loc @ PQ ) ) )
% 0.30/0.46 => ( eoutM @ PQ @ M @ E ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem5b_PQ
% 0.30/0.46 thf(fact_183_TBtheore54b__P,axiom,
% 0.30/0.46 ! [P: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.30/0.46 ( ( eoutM @ P @ M @ E )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.30/0.46 => ( ? [Ch3: secrecy_chanID] :
% 0.30/0.46 ( ( member @ secrecy_chanID @ Ch3 @ ( out @ Q ) )
% 0.30/0.46 & ( exprChannel @ Ch3 @ E )
% 0.30/0.46 & ~ ( member @ secrecy_chanID @ Ch3 @ ( loc @ PQ ) )
% 0.30/0.46 & ( member @ secrecy_chanID @ Ch3 @ M ) )
% 0.30/0.46 => ( eoutM @ PQ @ M @ E ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheore54b_P
% 0.30/0.46 thf(fact_184_TBtheorem5a__PQ,axiom,
% 0.30/0.46 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.30/0.46 ( ( ( eout @ P @ E )
% 0.30/0.46 | ( eout @ Q @ E ) )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.30/0.46 => ( ? [Ch3: secrecy_chanID] :
% 0.30/0.46 ( ( ( member @ secrecy_chanID @ Ch3 @ ( out @ P ) )
% 0.30/0.46 | ( member @ secrecy_chanID @ Ch3 @ ( out @ Q ) ) )
% 0.30/0.46 & ( exprChannel @ Ch3 @ E )
% 0.30/0.46 & ~ ( member @ secrecy_chanID @ Ch3 @ ( loc @ PQ ) ) )
% 0.30/0.46 => ( eout @ PQ @ E ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem5a_PQ
% 0.30/0.46 thf(fact_185_eout__def,axiom,
% 0.30/0.46 ( eout
% 0.30/0.46 = ( ^ [SP: secrecy_specID,E2: secrecy_Expression] :
% 0.30/0.46 ? [Ch2: secrecy_chanID] :
% 0.30/0.46 ( ( member @ secrecy_chanID @ Ch2 @ ( out @ SP ) )
% 0.30/0.46 & ( exprChannel @ Ch2 @ E2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eout_def
% 0.30/0.46 thf(fact_186_eoutM__def,axiom,
% 0.30/0.46 ( eoutM
% 0.30/0.46 = ( ^ [SP: secrecy_specID,M3: set @ secrecy_chanID,E2: secrecy_Expression] :
% 0.30/0.46 ? [Ch2: secrecy_chanID] :
% 0.30/0.46 ( ( member @ secrecy_chanID @ Ch2 @ ( out @ SP ) )
% 0.30/0.46 & ( member @ secrecy_chanID @ Ch2 @ M3 )
% 0.30/0.46 & ( exprChannel @ Ch2 @ E2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eoutM_def
% 0.30/0.46 thf(fact_187_out__exprChannelSet__def,axiom,
% 0.30/0.46 ( out_exprChannelSet
% 0.30/0.46 = ( ^ [SP: secrecy_specID,ChSet2: set @ secrecy_chanID,E2: secrecy_Expression] :
% 0.30/0.46 ( ! [X2: secrecy_chanID] :
% 0.30/0.46 ( ( member @ secrecy_chanID @ X2 @ ChSet2 )
% 0.30/0.46 => ( ( member @ secrecy_chanID @ X2 @ ( out @ SP ) )
% 0.30/0.46 & ( exprChannel @ X2 @ E2 ) ) )
% 0.30/0.46 & ! [X2: secrecy_chanID] :
% 0.30/0.46 ( ( ~ ( member @ secrecy_chanID @ X2 @ ChSet2 )
% 0.30/0.46 & ( member @ secrecy_chanID @ X2 @ ( out @ SP ) ) )
% 0.30/0.46 => ~ ( exprChannel @ X2 @ E2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % out_exprChannelSet_def
% 0.30/0.46 thf(fact_188_out__exprChannelSingle__def,axiom,
% 0.30/0.46 ( out_ex985543062Single
% 0.30/0.46 = ( ^ [SP: secrecy_specID,Ch2: secrecy_chanID,E2: secrecy_Expression] :
% 0.30/0.46 ( ( member @ secrecy_chanID @ Ch2 @ ( out @ SP ) )
% 0.30/0.46 & ( exprChannel @ Ch2 @ E2 )
% 0.30/0.46 & ! [X2: secrecy_chanID,T: nat] :
% 0.30/0.46 ( ( ( member @ secrecy_chanID @ X2 @ ( out @ SP ) )
% 0.30/0.46 & ( X2 != Ch2 ) )
% 0.30/0.46 => ~ ( exprChannel @ X2 @ E2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % out_exprChannelSingle_def
% 0.30/0.46 thf(fact_189_correctCompositionOut__prop1,axiom,
% 0.30/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,X: secrecy_chanID] :
% 0.30/0.46 ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.30/0.46 => ( ( member @ secrecy_chanID @ X @ ( out @ PQ ) )
% 0.30/0.46 => ( ( member @ secrecy_chanID @ X @ ( out @ P ) )
% 0.30/0.46 | ( member @ secrecy_chanID @ X @ ( out @ Q ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % correctCompositionOut_prop1
% 0.30/0.46 thf(fact_190_TBtheorem45a__P,axiom,
% 0.30/0.46 ! [P: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.30/0.46 ( ( eout @ P @ E )
% 0.30/0.46 => ( ( ( subcomponents @ PQ )
% 0.30/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.30/0.46 => ( ( correc990227761ionOut @ PQ )
% 0.30/0.46 => ( ? [Ch3: secrecy_chanID] :
% 0.30/0.46 ( ( member @ secrecy_chanID @ Ch3 @ ( out @ P ) )
% 0.30/0.46 & ( exprChannel @ Ch3 @ E )
% 0.30/0.46 & ~ ( member @ secrecy_chanID @ Ch3 @ ( loc @ PQ ) ) )
% 0.30/0.46 => ( eout @ PQ @ E ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % TBtheorem45a_P
% 0.30/0.46 thf(fact_191_adv__not__know2,axiom,
% 0.30/0.46 ! [P: secrecy_specID,A3: secrecy_specID,M2: secrecy_Secrets] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ secrecy_chanID ) @ ( out @ P ) @ ( ins @ A3 ) )
% 0.30/0.46 => ( ~ ( knowle1437066798e_know @ A3 @ ( secrecy_sKS @ M2 ) )
% 0.30/0.46 => ~ ( eout @ P @ ( secrecy_sE @ M2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % adv_not_know2
% 0.30/0.46 thf(fact_192_adv__not__know1,axiom,
% 0.30/0.46 ! [P: secrecy_specID,A3: secrecy_specID,M2: secrecy_Keys] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ secrecy_chanID ) @ ( out @ P ) @ ( ins @ A3 ) )
% 0.30/0.46 => ( ~ ( knowle1437066798e_know @ A3 @ ( secrecy_kKS @ M2 ) )
% 0.30/0.46 => ~ ( eout @ P @ ( secrecy_kE @ M2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % adv_not_know1
% 0.30/0.46 thf(fact_193_correctCompositionKeys__subcomp1,axiom,
% 0.30/0.46 ! [C4: secrecy_specID,X: secrecy_specID,Xb: secrecy_Keys] :
% 0.30/0.46 ( ( correc17873122onKeys @ C4 )
% 0.30/0.46 => ( ( member @ secrecy_specID @ X @ ( subcomponents @ C4 ) )
% 0.30/0.46 => ( ( member @ secrecy_Keys @ Xb @ ( specKeys @ C4 ) )
% 0.30/0.46 => ? [X3: secrecy_specID] :
% 0.30/0.46 ( ( member @ secrecy_specID @ X3 @ ( subcomponents @ C4 ) )
% 0.30/0.46 & ( member @ secrecy_Keys @ Xb @ ( specKeys @ X3 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % correctCompositionKeys_subcomp1
% 0.30/0.46 thf(fact_194_order__refl,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( preorder @ A )
% 0.30/0.46 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_refl
% 0.30/0.46 thf(fact_195_subset__antisym,axiom,
% 0.30/0.46 ! [A: $tType,A3: set @ A,B: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B )
% 0.30/0.46 => ( ( ord_less_eq @ ( set @ A ) @ B @ A3 )
% 0.30/0.46 => ( A3 = B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_antisym
% 0.30/0.46 thf(fact_196_subsetI,axiom,
% 0.30/0.46 ! [A: $tType,A3: set @ A,B: set @ A] :
% 0.30/0.46 ( ! [X3: A] :
% 0.30/0.46 ( ( member @ A @ X3 @ A3 )
% 0.30/0.46 => ( member @ A @ X3 @ B ) )
% 0.30/0.46 => ( ord_less_eq @ ( set @ A ) @ A3 @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 % subsetI
% 0.30/0.46 thf(fact_197_empty__subsetI,axiom,
% 0.30/0.46 ! [A: $tType,A3: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A3 ) ).
% 0.30/0.46
% 0.30/0.46 % empty_subsetI
% 0.30/0.46 thf(fact_198_subset__empty,axiom,
% 0.30/0.46 ! [A: $tType,A3: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ A3 @ ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 = ( A3
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_empty
% 0.30/0.46 thf(fact_199_insert__subset,axiom,
% 0.30/0.46 ! [A: $tType,X: A,A3: set @ A,B: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ X @ A3 ) @ B )
% 0.30/0.46 = ( ( member @ A @ X @ B )
% 0.30/0.46 & ( ord_less_eq @ ( set @ A ) @ A3 @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_subset
% 0.30/0.46 thf(fact_200_Un__subset__iff,axiom,
% 0.30/0.46 ! [A: $tType,A3: set @ A,B: set @ A,C4: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A3 @ B ) @ C4 )
% 0.30/0.46 = ( ( ord_less_eq @ ( set @ A ) @ A3 @ C4 )
% 0.30/0.46 & ( ord_less_eq @ ( set @ A ) @ B @ C4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_subset_iff
% 0.30/0.46 thf(fact_201_singleton__insert__inj__eq,axiom,
% 0.30/0.46 ! [A: $tType,B2: A,A2: A,A3: set @ A] :
% 0.30/0.46 ( ( ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 = ( insert @ A @ A2 @ A3 ) )
% 0.30/0.46 = ( ( A2 = B2 )
% 0.30/0.46 & ( ord_less_eq @ ( set @ A ) @ A3 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % singleton_insert_inj_eq
% 0.30/0.46 thf(fact_202_singleton__insert__inj__eq_H,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,A3: set @ A,B2: A] :
% 0.30/0.46 ( ( ( insert @ A @ A2 @ A3 )
% 0.30/0.46 = ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.46 = ( ( A2 = B2 )
% 0.30/0.46 & ( ord_less_eq @ ( set @ A ) @ A3 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % singleton_insert_inj_eq'
% 0.30/0.46 thf(fact_203_subset__singleton__iff,axiom,
% 0.30/0.46 ! [A: $tType,X4: set @ A,A2: A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ X4 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.46 = ( ( X4
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 | ( X4
% 0.30/0.46 = ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_singleton_iff
% 0.30/0.46 thf(fact_204_subset__singletonD,axiom,
% 0.30/0.46 ! [A: $tType,A3: set @ A,X: A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ A3 @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.30/0.46 => ( ( A3
% 0.30/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.30/0.46 | ( A3
% 0.30/0.46 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_singletonD
% 0.30/0.46 thf(fact_205_subset__Un__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) )
% 0.30/0.46 = ( ^ [A4: set @ A,B5: set @ A] :
% 0.30/0.46 ( ( sup_sup @ ( set @ A ) @ A4 @ B5 )
% 0.30/0.46 = B5 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_Un_eq
% 0.30/0.46 thf(fact_206_subset__UnE,axiom,
% 0.30/0.46 ! [A: $tType,C4: set @ A,A3: set @ A,B: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ C4 @ ( sup_sup @ ( set @ A ) @ A3 @ B ) )
% 0.30/0.46 => ~ ! [A6: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ A6 @ A3 )
% 0.30/0.46 => ! [B6: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ B6 @ B )
% 0.30/0.46 => ( C4
% 0.30/0.46 != ( sup_sup @ ( set @ A ) @ A6 @ B6 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_UnE
% 0.30/0.46 thf(fact_207_Un__absorb2,axiom,
% 0.30/0.46 ! [A: $tType,B: set @ A,A3: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ B @ A3 )
% 0.30/0.46 => ( ( sup_sup @ ( set @ A ) @ A3 @ B )
% 0.30/0.46 = A3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_absorb2
% 0.30/0.46 thf(fact_208_Un__absorb1,axiom,
% 0.30/0.46 ! [A: $tType,A3: set @ A,B: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B )
% 0.30/0.46 => ( ( sup_sup @ ( set @ A ) @ A3 @ B )
% 0.30/0.46 = B ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_absorb1
% 0.30/0.46 thf(fact_209_Un__upper2,axiom,
% 0.30/0.46 ! [A: $tType,B: set @ A,A3: set @ A] : ( ord_less_eq @ ( set @ A ) @ B @ ( sup_sup @ ( set @ A ) @ A3 @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_upper2
% 0.30/0.46 thf(fact_210_Un__upper1,axiom,
% 0.30/0.46 ! [A: $tType,A3: set @ A,B: set @ A] : ( ord_less_eq @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ A3 @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_upper1
% 0.30/0.46 thf(fact_211_Un__least,axiom,
% 0.30/0.46 ! [A: $tType,A3: set @ A,C4: set @ A,B: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ A3 @ C4 )
% 0.30/0.46 => ( ( ord_less_eq @ ( set @ A ) @ B @ C4 )
% 0.30/0.46 => ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A3 @ B ) @ C4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_least
% 0.30/0.46 thf(fact_212_Un__mono,axiom,
% 0.30/0.46 ! [A: $tType,A3: set @ A,C4: set @ A,B: set @ A,D3: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ A3 @ C4 )
% 0.30/0.46 => ( ( ord_less_eq @ ( set @ A ) @ B @ D3 )
% 0.30/0.46 => ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A3 @ B ) @ ( sup_sup @ ( set @ A ) @ C4 @ D3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Un_mono
% 0.30/0.46 thf(fact_213_bot_Oextremum__uniqueI,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order_bot @ A )
% 0.30/0.46 => ! [A2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ ( bot_bot @ A ) )
% 0.30/0.46 => ( A2
% 0.30/0.46 = ( bot_bot @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot.extremum_uniqueI
% 0.30/0.46 thf(fact_214_bot_Oextremum__unique,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order_bot @ A )
% 0.30/0.46 => ! [A2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ ( bot_bot @ A ) )
% 0.30/0.46 = ( A2
% 0.30/0.46 = ( bot_bot @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot.extremum_unique
% 0.30/0.46 thf(fact_215_bot_Oextremum,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order_bot @ A )
% 0.30/0.46 => ! [A2: A] : ( ord_less_eq @ A @ ( bot_bot @ A ) @ A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot.extremum
% 0.30/0.46 thf(fact_216_subset__insertI2,axiom,
% 0.30/0.46 ! [A: $tType,A3: set @ A,B: set @ A,B2: A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B )
% 0.30/0.46 => ( ord_less_eq @ ( set @ A ) @ A3 @ ( insert @ A @ B2 @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_insertI2
% 0.30/0.46 thf(fact_217_subset__insertI,axiom,
% 0.30/0.46 ! [A: $tType,B: set @ A,A2: A] : ( ord_less_eq @ ( set @ A ) @ B @ ( insert @ A @ A2 @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_insertI
% 0.30/0.46 thf(fact_218_subset__insert,axiom,
% 0.30/0.46 ! [A: $tType,X: A,A3: set @ A,B: set @ A] :
% 0.30/0.46 ( ~ ( member @ A @ X @ A3 )
% 0.30/0.46 => ( ( ord_less_eq @ ( set @ A ) @ A3 @ ( insert @ A @ X @ B ) )
% 0.30/0.46 = ( ord_less_eq @ ( set @ A ) @ A3 @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_insert
% 0.30/0.46 thf(fact_219_insert__mono,axiom,
% 0.30/0.46 ! [A: $tType,C4: set @ A,D3: set @ A,A2: A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ C4 @ D3 )
% 0.30/0.46 => ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ A2 @ C4 ) @ ( insert @ A @ A2 @ D3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_mono
% 0.30/0.46 thf(fact_220_dual__order_Oantisym,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [B2: A,A2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ( A2 = B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.antisym
% 0.30/0.46 thf(fact_221_dual__order_Oeq__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ( ( ^ [Y3: A,Z: A] : ( Y3 = Z ) )
% 0.30/0.46 = ( ^ [A5: A,B7: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ B7 @ A5 )
% 0.30/0.46 & ( ord_less_eq @ A @ A5 @ B7 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.eq_iff
% 0.30/0.46 thf(fact_222_dual__order_Otrans,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [B2: A,A2: A,C: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ C @ B2 )
% 0.30/0.46 => ( ord_less_eq @ A @ C @ A2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.trans
% 0.30/0.46 thf(fact_223_linorder__wlog,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [P: A > A > $o,A2: A,B2: A] :
% 0.30/0.46 ( ! [A7: A,B8: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A7 @ B8 )
% 0.30/0.46 => ( P @ A7 @ B8 ) )
% 0.30/0.46 => ( ! [A7: A,B8: A] :
% 0.30/0.46 ( ( P @ B8 @ A7 )
% 0.30/0.46 => ( P @ A7 @ B8 ) )
% 0.30/0.46 => ( P @ A2 @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % linorder_wlog
% 0.30/0.46 thf(fact_224_dual__order_Orefl,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.refl
% 0.30/0.46 thf(fact_225_order__trans,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( preorder @ A )
% 0.30/0.46 => ! [X: A,Y2: A,Z2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X @ Y2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ Y2 @ Z2 )
% 0.30/0.46 => ( ord_less_eq @ A @ X @ Z2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_trans
% 0.30/0.46 thf(fact_226_order__class_Oorder_Oantisym,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.30/0.46 => ( A2 = B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_class.order.antisym
% 0.30/0.46 thf(fact_227_ord__le__eq__trans,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ord @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( B2 = C )
% 0.30/0.46 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_le_eq_trans
% 0.30/0.46 thf(fact_228_ord__eq__le__trans,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ord @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C: A] :
% 0.30/0.46 ( ( A2 = B2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ B2 @ C )
% 0.30/0.46 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_eq_le_trans
% 0.30/0.46 thf(fact_229_order__class_Oorder_Oeq__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ( ( ^ [Y3: A,Z: A] : ( Y3 = Z ) )
% 0.30/0.46 = ( ^ [A5: A,B7: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A5 @ B7 )
% 0.30/0.46 & ( ord_less_eq @ A @ B7 @ A5 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_class.order.eq_iff
% 0.30/0.46 thf(fact_230_antisym__conv,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [Y2: A,X: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ Y2 @ X )
% 0.30/0.46 => ( ( ord_less_eq @ A @ X @ Y2 )
% 0.30/0.46 = ( X = Y2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % antisym_conv
% 0.30/0.46 thf(fact_231_le__cases3,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [X: A,Y2: A,Z2: A] :
% 0.30/0.46 ( ( ( ord_less_eq @ A @ X @ Y2 )
% 0.30/0.46 => ~ ( ord_less_eq @ A @ Y2 @ Z2 ) )
% 0.30/0.46 => ( ( ( ord_less_eq @ A @ Y2 @ X )
% 0.30/0.46 => ~ ( ord_less_eq @ A @ X @ Z2 ) )
% 0.30/0.46 => ( ( ( ord_less_eq @ A @ X @ Z2 )
% 0.30/0.46 => ~ ( ord_less_eq @ A @ Z2 @ Y2 ) )
% 0.30/0.46 => ( ( ( ord_less_eq @ A @ Z2 @ Y2 )
% 0.30/0.46 => ~ ( ord_less_eq @ A @ Y2 @ X ) )
% 0.30/0.46 => ( ( ( ord_less_eq @ A @ Y2 @ Z2 )
% 0.30/0.46 => ~ ( ord_less_eq @ A @ Z2 @ X ) )
% 0.30/0.46 => ~ ( ( ord_less_eq @ A @ Z2 @ X )
% 0.30/0.46 => ~ ( ord_less_eq @ A @ X @ Y2 ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_cases3
% 0.30/0.46 thf(fact_232_order_Otrans,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ B2 @ C )
% 0.30/0.46 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order.trans
% 0.30/0.46 thf(fact_233_le__cases,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [X: A,Y2: A] :
% 0.30/0.46 ( ~ ( ord_less_eq @ A @ X @ Y2 )
% 0.30/0.46 => ( ord_less_eq @ A @ Y2 @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_cases
% 0.30/0.46 thf(fact_234_eq__refl,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( preorder @ A )
% 0.30/0.46 => ! [X: A,Y2: A] :
% 0.30/0.46 ( ( X = Y2 )
% 0.30/0.46 => ( ord_less_eq @ A @ X @ Y2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eq_refl
% 0.30/0.46 thf(fact_235_linear,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [X: A,Y2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X @ Y2 )
% 0.30/0.46 | ( ord_less_eq @ A @ Y2 @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % linear
% 0.30/0.46 thf(fact_236_antisym,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [X: A,Y2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X @ Y2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ Y2 @ X )
% 0.30/0.46 => ( X = Y2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % antisym
% 0.30/0.46 thf(fact_237_eq__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ( ( ^ [Y3: A,Z: A] : ( Y3 = Z ) )
% 0.30/0.46 = ( ^ [X2: A,Y4: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X2 @ Y4 )
% 0.30/0.46 & ( ord_less_eq @ A @ Y4 @ X2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eq_iff
% 0.30/0.46 thf(fact_238_ord__le__eq__subst,axiom,
% 0.30/0.46 ! [A: $tType,B3: $tType] :
% 0.30/0.46 ( ( ( ord @ B3 )
% 0.30/0.46 & ( ord @ A ) )
% 0.30/0.46 => ! [A2: A,B2: A,F: A > B3,C: B3] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( ( F @ B2 )
% 0.30/0.46 = C )
% 0.30/0.46 => ( ! [X3: A,Y: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X3 @ Y )
% 0.30/0.46 => ( ord_less_eq @ B3 @ ( F @ X3 ) @ ( F @ Y ) ) )
% 0.30/0.46 => ( ord_less_eq @ B3 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_le_eq_subst
% 0.30/0.46 thf(fact_239_ord__eq__le__subst,axiom,
% 0.30/0.46 ! [A: $tType,B3: $tType] :
% 0.30/0.46 ( ( ( ord @ B3 )
% 0.30/0.46 & ( ord @ A ) )
% 0.30/0.46 => ! [A2: A,F: B3 > A,B2: B3,C: B3] :
% 0.30/0.46 ( ( A2
% 0.30/0.46 = ( F @ B2 ) )
% 0.30/0.46 => ( ( ord_less_eq @ B3 @ B2 @ C )
% 0.30/0.46 => ( ! [X3: B3,Y: B3] :
% 0.30/0.46 ( ( ord_less_eq @ B3 @ X3 @ Y )
% 0.30/0.46 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y ) ) )
% 0.30/0.46 => ( ord_less_eq @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_eq_le_subst
% 0.30/0.46 thf(fact_240_order__subst2,axiom,
% 0.30/0.46 ! [A: $tType,C2: $tType] :
% 0.30/0.46 ( ( ( order @ C2 )
% 0.30/0.46 & ( order @ A ) )
% 0.30/0.46 => ! [A2: A,B2: A,F: A > C2,C: C2] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( ord_less_eq @ C2 @ ( F @ B2 ) @ C )
% 0.30/0.46 => ( ! [X3: A,Y: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X3 @ Y )
% 0.30/0.46 => ( ord_less_eq @ C2 @ ( F @ X3 ) @ ( F @ Y ) ) )
% 0.30/0.46 => ( ord_less_eq @ C2 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_subst2
% 0.30/0.46 thf(fact_241_order__subst1,axiom,
% 0.30/0.46 ! [A: $tType,B3: $tType] :
% 0.30/0.46 ( ( ( order @ B3 )
% 0.30/0.46 & ( order @ A ) )
% 0.30/0.46 => ! [A2: A,F: B3 > A,B2: B3,C: B3] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ ( F @ B2 ) )
% 0.30/0.46 => ( ( ord_less_eq @ B3 @ B2 @ C )
% 0.30/0.46 => ( ! [X3: B3,Y: B3] :
% 0.30/0.46 ( ( ord_less_eq @ B3 @ X3 @ Y )
% 0.30/0.46 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y ) ) )
% 0.30/0.46 => ( ord_less_eq @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_subst1
% 0.30/0.46 thf(fact_242_Collect__mono__iff,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 0.30/0.46 = ( ! [X2: A] :
% 0.30/0.46 ( ( P @ X2 )
% 0.30/0.46 => ( Q @ X2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_mono_iff
% 0.30/0.46 thf(fact_243_le__fun__def,axiom,
% 0.30/0.46 ! [B3: $tType,A: $tType] :
% 0.30/0.46 ( ( ord @ B3 )
% 0.30/0.46 => ( ( ord_less_eq @ ( A > B3 ) )
% 0.30/0.46 = ( ^ [F2: A > B3,G2: A > B3] :
% 0.30/0.46 ! [X2: A] : ( ord_less_eq @ B3 @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_fun_def
% 0.30/0.46 thf(fact_244_set__eq__subset,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ^ [Y3: set @ A,Z: set @ A] : ( Y3 = Z ) )
% 0.30/0.46 = ( ^ [A4: set @ A,B5: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.30/0.46 & ( ord_less_eq @ ( set @ A ) @ B5 @ A4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % set_eq_subset
% 0.30/0.46 thf(fact_245_le__funI,axiom,
% 0.30/0.46 ! [B3: $tType,A: $tType] :
% 0.30/0.46 ( ( ord @ B3 )
% 0.30/0.46 => ! [F: A > B3,G: A > B3] :
% 0.30/0.46 ( ! [X3: A] : ( ord_less_eq @ B3 @ ( F @ X3 ) @ ( G @ X3 ) )
% 0.30/0.46 => ( ord_less_eq @ ( A > B3 ) @ F @ G ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_funI
% 0.30/0.46 thf(fact_246_le__funE,axiom,
% 0.30/0.46 ! [B3: $tType,A: $tType] :
% 0.30/0.46 ( ( ord @ B3 )
% 0.30/0.46 => ! [F: A > B3,G: A > B3,X: A] :
% 0.30/0.46 ( ( ord_less_eq @ ( A > B3 ) @ F @ G )
% 0.30/0.46 => ( ord_less_eq @ B3 @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_funE
% 0.30/0.46 thf(fact_247_le__funD,axiom,
% 0.30/0.46 ! [B3: $tType,A: $tType] :
% 0.30/0.46 ( ( ord @ B3 )
% 0.30/0.46 => ! [F: A > B3,G: A > B3,X: A] :
% 0.30/0.46 ( ( ord_less_eq @ ( A > B3 ) @ F @ G )
% 0.30/0.46 => ( ord_less_eq @ B3 @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_funD
% 0.30/0.46 thf(fact_248_subset__trans,axiom,
% 0.30/0.46 ! [A: $tType,A3: set @ A,B: set @ A,C4: set @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B )
% 0.30/0.46 => ( ( ord_less_eq @ ( set @ A ) @ B @ C4 )
% 0.30/0.46 => ( ord_less_eq @ ( set @ A ) @ A3 @ C4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_trans
% 0.30/0.46 thf(fact_249_Collect__mono,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.30/0.46 ( ! [X3: A] :
% 0.30/0.46 ( ( P @ X3 )
% 0.30/0.46 => ( Q @ X3 ) )
% 0.30/0.46 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_mono
% 0.30/0.46 thf(fact_250_subset__refl,axiom,
% 0.30/0.46 ! [A: $tType,A3: set @ A] : ( ord_less_eq @ ( set @ A ) @ A3 @ A3 ) ).
% 0.30/0.46
% 0.30/0.46 % subset_refl
% 0.30/0.46 thf(fact_251_subset__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) )
% 0.30/0.46 = ( ^ [A4: set @ A,B5: set @ A] :
% 0.30/0.46 ! [T: A] :
% 0.30/0.46 ( ( member @ A @ T @ A4 )
% 0.30/0.46 => ( member @ A @ T @ B5 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_iff
% 0.30/0.46 thf(fact_252_equalityD2,axiom,
% 0.30/0.46 ! [A: $tType,A3: set @ A,B: set @ A] :
% 0.30/0.46 ( ( A3 = B )
% 0.30/0.46 => ( ord_less_eq @ ( set @ A ) @ B @ A3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % equalityD2
% 0.30/0.46 thf(fact_253_equalityD1,axiom,
% 0.30/0.46 ! [A: $tType,A3: set @ A,B: set @ A] :
% 0.30/0.46 ( ( A3 = B )
% 0.30/0.46 => ( ord_less_eq @ ( set @ A ) @ A3 @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 % equalityD1
% 0.30/0.46 thf(fact_254_subset__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ord_less_eq @ ( set @ A ) )
% 0.30/0.46 = ( ^ [A4: set @ A,B5: set @ A] :
% 0.30/0.46 ! [X2: A] :
% 0.30/0.46 ( ( member @ A @ X2 @ A4 )
% 0.30/0.46 => ( member @ A @ X2 @ B5 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % subset_eq
% 0.30/0.46 thf(fact_255_equalityE,axiom,
% 0.30/0.46 ! [A: $tType,A3: set @ A,B: set @ A] :
% 0.30/0.46 ( ( A3 = B )
% 0.30/0.46 => ~ ( ( ord_less_eq @ ( set @ A ) @ A3 @ B )
% 0.30/0.46 => ~ ( ord_less_eq @ ( set @ A ) @ B @ A3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % equalityE
% 0.30/0.46
% 0.30/0.46 % Type constructors (28)
% 0.30/0.46 thf(tcon_HOL_Obool___Lattices_Obounded__lattice,axiom,
% 0.30/0.46 bounded_lattice @ $o ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1,axiom,
% 0.30/0.46 ! [A8: $tType] : ( bounded_lattice @ ( set @ A8 ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_fun___Lattices_Obounded__lattice_2,axiom,
% 0.30/0.46 ! [A8: $tType,A9: $tType] :
% 0.30/0.46 ( ( bounded_lattice @ A9 )
% 0.30/0.46 => ( bounded_lattice @ ( A8 > A9 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_fun___Lattices_Obounded__semilattice__sup__bot,axiom,
% 0.30/0.46 ! [A8: $tType,A9: $tType] :
% 0.30/0.46 ( ( bounded_lattice @ A9 )
% 0.30/0.46 => ( bounde1808546759up_bot @ ( A8 > A9 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_fun___Orderings_Oorder__bot,axiom,
% 0.30/0.46 ! [A8: $tType,A9: $tType] :
% 0.30/0.46 ( ( order_bot @ A9 )
% 0.30/0.46 => ( order_bot @ ( A8 > A9 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.30/0.46 ! [A8: $tType,A9: $tType] :
% 0.30/0.46 ( ( preorder @ A9 )
% 0.30/0.46 => ( preorder @ ( A8 > A9 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.30/0.46 ! [A8: $tType,A9: $tType] :
% 0.30/0.46 ( ( order @ A9 )
% 0.30/0.46 => ( order @ ( A8 > A9 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_fun___Orderings_Oord,axiom,
% 0.30/0.46 ! [A8: $tType,A9: $tType] :
% 0.30/0.46 ( ( ord @ A9 )
% 0.30/0.46 => ( ord @ ( A8 > A9 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_fun___Orderings_Obot,axiom,
% 0.30/0.46 ! [A8: $tType,A9: $tType] :
% 0.30/0.46 ( ( bot @ A9 )
% 0.30/0.46 => ( bot @ ( A8 > A9 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Orderings_Oorder__bot_3,axiom,
% 0.30/0.46 order_bot @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Orderings_Opreorder_4,axiom,
% 0.30/0.46 preorder @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 0.30/0.46 linorder @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Orderings_Oorder_5,axiom,
% 0.30/0.46 order @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Orderings_Oord_6,axiom,
% 0.30/0.46 ord @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Orderings_Obot_7,axiom,
% 0.30/0.46 bot @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_8,axiom,
% 0.30/0.46 ! [A8: $tType] : ( bounde1808546759up_bot @ ( set @ A8 ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Set_Oset___Orderings_Oorder__bot_9,axiom,
% 0.30/0.46 ! [A8: $tType] : ( order_bot @ ( set @ A8 ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Set_Oset___Orderings_Opreorder_10,axiom,
% 0.30/0.46 ! [A8: $tType] : ( preorder @ ( set @ A8 ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Set_Oset___Orderings_Oorder_11,axiom,
% 0.30/0.46 ! [A8: $tType] : ( order @ ( set @ A8 ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Set_Oset___Orderings_Oord_12,axiom,
% 0.30/0.46 ! [A8: $tType] : ( ord @ ( set @ A8 ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Set_Oset___Orderings_Obot_13,axiom,
% 0.30/0.46 ! [A8: $tType] : ( bot @ ( set @ A8 ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_14,axiom,
% 0.30/0.46 bounde1808546759up_bot @ $o ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Orderings_Oorder__bot_15,axiom,
% 0.30/0.46 order_bot @ $o ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Orderings_Opreorder_16,axiom,
% 0.30/0.46 preorder @ $o ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Orderings_Olinorder_17,axiom,
% 0.30/0.46 linorder @ $o ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Orderings_Oorder_18,axiom,
% 0.30/0.46 order @ $o ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Orderings_Oord_19,axiom,
% 0.30/0.46 ord @ $o ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Orderings_Obot_20,axiom,
% 0.30/0.46 bot @ $o ).
% 0.30/0.46
% 0.30/0.46 % Conjectures (1)
% 0.30/0.46 thf(conj_0,conjecture,
% 0.30/0.46 ~ ( member @ secrecy_KS @ m @ ( specKeysSecrets @ pq ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 3.01/1.52 ---- Embedded in THF ---
% 3.01/1.52 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.01/1.52 %%% Generated on Tue Feb 24 08:26:13 EST 2026
% 3.01/1.52 %%% using '$$dhol' embedding, version 1.3.0.
% 3.01/1.52 %%% Logic specification used:
% 3.01/1.52 %%% thf(spec, logic, $$dhol).
% 3.01/1.52
% 3.01/1.52 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.OaDn1w6qtU/DTF2DTF5010.p
% 3.01/1.52 thf(ty_t_Secrecy__types_OExpression, type, secrecy_Expression: $tType).
% 3.01/1.52 thf(ty_t_Secrecy__types_OSecrets, type, secrecy_Secrets: $tType).
% 3.01/1.52 thf(ty_t_Secrecy__types_OspecID, type, secrecy_specID: $tType).
% 3.01/1.52 thf(ty_t_Secrecy__types_OchanID, type, secrecy_chanID: $tType).
% 3.01/1.52 thf(ty_t_Secrecy__types_OKeys, type, secrecy_Keys: $tType).
% 3.01/1.52 thf(ty_t_Secrecy__types_OKS, type, secrecy_KS: $tType).
% 3.01/1.52 thf(ty_t_List_Olist, type, list: ($tType > $tType)).
% 3.01/1.52 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 3.01/1.52 thf(ty_t_Nat_Onat, type, nat: $tType).
% 3.01/1.52 thf(sy_cl_Lattices_Obounded__lattice, type, bounded_lattice: (!> [A:$tType]: ($o))).
% 3.01/1.52 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 3.01/1.52 thf(sy_cl_Orderings_Obot, type, bot: (!> [A:$tType]: ($o))).
% 3.01/1.52 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: ($o))).
% 3.01/1.52 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: ($o))).
% 3.01/1.52 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 3.01/1.52 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: ($o))).
% 3.01/1.52 thf(sy_cl_Orderings_Oorder__bot, type, order_bot: (!> [A:$tType]: ($o))).
% 3.01/1.52 thf(sy_cl_Lattices_Obounded__semilattice__sup__bot, type, bounde1808546759up_bot: (!> [A:$tType]: ($o))).
% 3.01/1.52 thf(sy_c_CompLocalSecrets_OLocalSecrets, type, localSecrets: (secrecy_specID > (set @ secrecy_KS))).
% 3.01/1.52 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__khazhniute_OeoutKnowCorrect, type, knowle1667810483orrect: (secrecy_specID > (secrecy_KS > $o))).
% 3.01/1.52 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__khazhniute_Oknow, type, knowle1437066798e_know: (secrecy_specID > (secrecy_KS > $o))).
% 3.01/1.52 thf(sy_c_Lattices_Osup__class_Osup, type, sup_sup: (!> [A:$tType]: ((A > (A > A))))).
% 3.01/1.52 thf(sy_c_ListExtras_Omem, type, mem: (!> [A:$tType]: ((A > ((list @ A) > $o))))).
% 3.01/1.52 thf(sy_c_Orderings_Obot__class_Obot, type, bot_bot: (!> [A:$tType]: (A))).
% 3.01/1.52 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 3.01/1.52 thf(sy_c_Secrecy_OcorrectCompositionKS, type, correctCompositionKS: (secrecy_specID > $o)).
% 3.01/1.52 thf(sy_c_Secrecy_OcorrectCompositionKeys, type, correc17873122onKeys: (secrecy_specID > $o)).
% 3.01/1.52 thf(sy_c_Secrecy_Oeout, type, eout: (secrecy_specID > (secrecy_Expression > $o))).
% 3.01/1.52 thf(sy_c_Secrecy_OeoutM, type, eoutM: (secrecy_specID > ((set @ secrecy_chanID) > (secrecy_Expression > $o)))).
% 3.01/1.52 thf(sy_c_Secrecy_OexprChannel, type, exprChannel: (secrecy_chanID > (secrecy_Expression > $o))).
% 3.01/1.52 thf(sy_c_Secrecy_Oine, type, ine: (secrecy_specID > (secrecy_Expression > $o))).
% 3.01/1.52 thf(sy_c_Secrecy_OineM, type, ineM: (secrecy_specID > ((set @ secrecy_chanID) > (secrecy_Expression > $o)))).
% 3.01/1.52 thf(sy_c_Secrecy_Oine__exprChannelSet, type, ine_exprChannelSet: (secrecy_specID > ((set @ secrecy_chanID) > (secrecy_Expression > $o)))).
% 3.01/1.52 thf(sy_c_Secrecy_Oine__exprChannelSingle, type, ine_ex1303305700Single: (secrecy_specID > (secrecy_chanID > (secrecy_Expression > $o)))).
% 3.01/1.52 thf(sy_c_Secrecy_OnotSpecKeysSecretsExpr, type, notSpe1586871396tsExpr: (secrecy_specID > ((list @ secrecy_Expression) > $o))).
% 3.01/1.52 thf(sy_c_Secrecy_Oout__exprChannelSet, type, out_exprChannelSet: (secrecy_specID > ((set @ secrecy_chanID) > (secrecy_Expression > $o)))).
% 3.01/1.52 thf(sy_c_Secrecy_Oout__exprChannelSingle, type, out_ex985543062Single: (secrecy_specID > (secrecy_chanID > (secrecy_Expression > $o)))).
% 3.01/1.52 thf(sy_c_Secrecy_OspecKeys, type, specKeys: (secrecy_specID > (set @ secrecy_Keys))).
% 3.01/1.52 thf(sy_c_Secrecy_OspecKeysSecrets, type, specKeysSecrets: (secrecy_specID > (set @ secrecy_KS))).
% 3.01/1.52 thf(sy_c_Secrecy_OspecSecrets, type, specSecrets: (secrecy_specID > (set @ secrecy_Secrets))).
% 3.01/1.52 thf(sy_c_Secrecy__types_OExpression_OkE, type, secrecy_kE: (secrecy_Keys > secrecy_Expression)).
% 3.01/1.52 thf(sy_c_Secrecy__types_OExpression_OsE, type, secrecy_sE: (secrecy_Secrets > secrecy_Expression)).
% 3.01/1.52 thf(sy_c_Secrecy__types_OKS2Expression, type, secrec1016742679ession: (secrecy_KS > secrecy_Expression)).
% 3.01/1.52 thf(sy_c_Secrecy__types_OKS_OkKS, type, secrecy_kKS: (secrecy_Keys > secrecy_KS)).
% 3.01/1.52 thf(sy_c_Secrecy__types_OKS_OsKS, type, secrecy_sKS: (secrecy_Secrets > secrecy_KS)).
% 3.01/1.52 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 3.01/1.52 thf(sy_c_Set_Oinsert, type, insert: (!> [A:$tType]: ((A > ((set @ A) > (set @ A)))))).
% 3.01/1.52 thf(sy_c_Set_Ois__empty, type, is_empty: (!> [A:$tType]: (((set @ A) > $o)))).
% 3.01/1.52 thf(sy_c_Set_Ois__singleton, type, is_singleton: (!> [A:$tType]: (((set @ A) > $o)))).
% 3.01/1.52 thf(sy_c_Set_Othe__elem, type, the_elem: (!> [A:$tType]: (((set @ A) > A)))).
% 3.01/1.52 thf(sy_c_inout_OcorrectCompositionIn, type, correctCompositionIn: (secrecy_specID > $o)).
% 3.01/1.52 thf(sy_c_inout_OcorrectCompositionLoc, type, correc965049635ionLoc: (secrecy_specID > $o)).
% 3.01/1.52 thf(sy_c_inout_OcorrectCompositionOut, type, correc990227761ionOut: (secrecy_specID > $o)).
% 3.01/1.52 thf(sy_c_inout_OinStream, type, inStream: (secrecy_specID > ((set @ secrecy_chanID) > $o))).
% 3.01/1.52 thf(sy_c_inout_Oins, type, ins: (secrecy_specID > (set @ secrecy_chanID))).
% 3.01/1.52 thf(sy_c_inout_Oloc, type, loc: (secrecy_specID > (set @ secrecy_chanID))).
% 3.01/1.52 thf(sy_c_inout_OlocStream, type, locStream: (secrecy_specID > ((set @ secrecy_chanID) > $o))).
% 3.01/1.52 thf(sy_c_inout_Oout, type, out: (secrecy_specID > (set @ secrecy_chanID))).
% 3.01/1.52 thf(sy_c_inout_Osubcomponents, type, subcomponents: (secrecy_specID > (set @ secrecy_specID))).
% 3.01/1.52 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 3.01/1.52 thf(sy_v_P, type, p: secrecy_specID).
% 3.01/1.52 thf(sy_v_PQ, type, pq: secrecy_specID).
% 3.01/1.52 thf(sy_v_Q, type, q: secrecy_specID).
% 3.01/1.52 thf(sy_v_key____, type, key: secrecy_Keys).
% 3.01/1.52 thf(sy_v_m, type, m: secrecy_KS).
% 3.01/1.52 thf(fact_0_cCompKS, axiom, (correctCompositionKS @ pq)).
% 3.01/1.52 thf(fact_1_notKSQ, axiom, (~ ((((member @ secrecy_KS) @ m) @ (specKeysSecrets @ q))))).
% 3.01/1.52 thf(fact_2_notKSP, axiom, (~ ((((member @ secrecy_KS) @ m) @ (specKeysSecrets @ p))))).
% 3.01/1.52 thf(fact_3_subPQ, axiom, ((subcomponents @ pq) = (((insert @ secrecy_specID) @ p) @ (((insert @ secrecy_specID) @ q) @ (bot_bot @ (set @ secrecy_specID)))))).
% 3.01/1.52 thf(fact_4_cCompI, axiom, (correctCompositionIn @ pq)).
% 3.01/1.52 thf(fact_5_assms_I3_J, axiom, ((knowle1437066798e_know @ p) @ m)).
% 3.01/1.52 thf(fact_6_a1, axiom, (m = (secrecy_kKS @ key))).
% 3.01/1.52 thf(fact_7_correctCompositionKS__PQ, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Ks:secrecy_KS]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionKS @ PQ) => ((((member @ secrecy_KS) @ Ks) @ (specKeysSecrets @ PQ)) => ((((member @ secrecy_KS) @ Ks) @ (specKeysSecrets @ P)) | (((member @ secrecy_KS) @ Ks) @ (specKeysSecrets @ Q))))))))).
% 3.01/1.52 thf(fact_8_correctCompositionKS__neg1, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Ks:secrecy_KS]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionKS @ PQ) => ((~ ((((member @ secrecy_KS) @ Ks) @ (specKeysSecrets @ P)))) => ((~ ((((member @ secrecy_KS) @ Ks) @ (specKeysSecrets @ Q)))) => (~ ((((member @ secrecy_KS) @ Ks) @ (specKeysSecrets @ PQ))))))))))).
% 3.01/1.52 thf(fact_9_correctCompositionKS__negP, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Ks:secrecy_KS]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionKS @ PQ) => ((~ ((((member @ secrecy_KS) @ Ks) @ (specKeysSecrets @ PQ)))) => (~ ((((member @ secrecy_KS) @ Ks) @ (specKeysSecrets @ P)))))))))).
% 3.01/1.52 thf(fact_10_correctCompositionKS__negQ, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Ks:secrecy_KS]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionKS @ PQ) => ((~ ((((member @ secrecy_KS) @ Ks) @ (specKeysSecrets @ PQ)))) => (~ ((((member @ secrecy_KS) @ Ks) @ (specKeysSecrets @ Q)))))))))).
% 3.01/1.52 thf(fact_11_singletonI, axiom, (! [A:$tType,A2:A]: ((((member @ A) @ A2) @ (((insert @ A) @ A2) @ (bot_bot @ (set @ A))))))).
% 3.01/1.52 thf(fact_12_KS_Oinject_I1_J, axiom, (! [X1:secrecy_Keys,Y1:secrecy_Keys]: ((((secrecy_kKS @ X1) = (secrecy_kKS @ Y1)) = (X1 = Y1))))).
% 3.01/1.52 thf(fact_13_insertCI, axiom, (! [A:$tType,A2:A,B:(set @ A),B2:A]: ((((~ ((((member @ A) @ A2) @ B))) => (A2 = B2)) => (((member @ A) @ A2) @ (((insert @ A) @ B2) @ B)))))).
% 3.01/1.52 thf(fact_14_insert__iff, axiom, (! [A:$tType,A2:A,B2:A,A3:(set @ A)]: (((((member @ A) @ A2) @ (((insert @ A) @ B2) @ A3)) = ((A2 = B2) | (((member @ A) @ A2) @ A3)))))).
% 3.01/1.52 thf(fact_15_insert__absorb2, axiom, (! [A:$tType,X:A,A3:(set @ A)]: (((((insert @ A) @ X) @ (((insert @ A) @ X) @ A3)) = (((insert @ A) @ X) @ A3))))).
% 3.01/1.52 thf(fact_16_empty__iff, axiom, (! [A:$tType,C:A]: ((~ ((((member @ A) @ C) @ (bot_bot @ (set @ A)))))))).
% 3.01/1.52 thf(fact_17_all__not__in__conv, axiom, (! [A:$tType,A3:(set @ A)]: (((! [X2:A]: ((~ ((((member @ A) @ X2) @ A3))))) = (A3 = (bot_bot @ (set @ A))))))).
% 3.01/1.52 thf(fact_18_Collect__empty__eq, axiom, (! [A:$tType,P:(A > $o)]: (((((collect @ A) @ P) = (bot_bot @ (set @ A))) = (! [X2:A]: ((~ ((P @ X2))))))))).
% 3.01/1.52 thf(fact_19_empty__Collect__eq, axiom, (! [A:$tType,P:(A > $o)]: ((((bot_bot @ (set @ A)) = ((collect @ A) @ P)) = (! [X2:A]: ((~ ((P @ X2))))))))).
% 3.01/1.52 thf(fact_20_bot__apply, axiom, (! [C2:$tType,D:$tType]: (((bot @ C2) => ((bot_bot @ (D > C2)) = (^ [X2:D]: ((bot_bot @ C2)))))))).
% 3.01/1.52 thf(fact_21_singletonD, axiom, (! [A:$tType,B2:A,A2:A]: (((((member @ A) @ B2) @ (((insert @ A) @ A2) @ (bot_bot @ (set @ A)))) => (B2 = A2))))).
% 3.01/1.52 thf(fact_22_bot__set__def, axiom, (! [A:$tType]: (((bot_bot @ (set @ A)) = ((collect @ A) @ (bot_bot @ (A > $o))))))).
% 3.01/1.52 thf(fact_23_bot__fun__def, axiom, (! [B3:$tType,A:$tType]: (((bot @ B3) => ((bot_bot @ (A > B3)) = (^ [X2:A]: ((bot_bot @ B3)))))))).
% 3.01/1.52 thf(fact_24_ex__in__conv, axiom, (! [A:$tType,A3:(set @ A)]: (((? [X2:A]: ((((member @ A) @ X2) @ A3))) = (A3 != (bot_bot @ (set @ A))))))).
% 3.01/1.52 thf(fact_25_equals0I, axiom, (! [A:$tType,A3:(set @ A)]: (((! [Y:A]: ((~ ((((member @ A) @ Y) @ A3))))) => (A3 = (bot_bot @ (set @ A))))))).
% 3.01/1.52 thf(fact_26_equals0D, axiom, (! [A:$tType,A3:(set @ A),A2:A]: (((A3 = (bot_bot @ (set @ A))) => (~ ((((member @ A) @ A2) @ A3))))))).
% 3.01/1.52 thf(fact_27_emptyE, axiom, (! [A:$tType,A2:A]: ((~ ((((member @ A) @ A2) @ (bot_bot @ (set @ A)))))))).
% 3.01/1.52 thf(fact_28_mk__disjoint__insert, axiom, (! [A:$tType,A2:A,A3:(set @ A)]: (((((member @ A) @ A2) @ A3) => (? [B4:(set @ A)]: (((A3 = (((insert @ A) @ A2) @ B4)) & (~ ((((member @ A) @ A2) @ B4)))))))))).
% 3.01/1.52 thf(fact_29_insert__commute, axiom, (! [A:$tType,X:A,Y2:A,A3:(set @ A)]: (((((insert @ A) @ X) @ (((insert @ A) @ Y2) @ A3)) = (((insert @ A) @ Y2) @ (((insert @ A) @ X) @ A3)))))).
% 3.01/1.52 thf(fact_30_insert__eq__iff, axiom, (! [A:$tType,A2:A,A3:(set @ A),B2:A,B:(set @ A)]: (((~ ((((member @ A) @ A2) @ A3))) => ((~ ((((member @ A) @ B2) @ B))) => (((((insert @ A) @ A2) @ A3) = (((insert @ A) @ B2) @ B)) = (((A2 = B2) => (A3 = B)) & ((A2 != B2) => (? [C3:(set @ A)]: (((A3 = (((insert @ A) @ B2) @ C3)) & ((~ ((((member @ A) @ B2) @ C3))) & ((B = (((insert @ A) @ A2) @ C3)) & (~ ((((member @ A) @ A2) @ C3)))))))))))))))).
% 3.01/1.52 thf(fact_31_insert__absorb, axiom, (! [A:$tType,A2:A,A3:(set @ A)]: (((((member @ A) @ A2) @ A3) => ((((insert @ A) @ A2) @ A3) = A3))))).
% 3.01/1.52 thf(fact_32_insert__ident, axiom, (! [A:$tType,X:A,A3:(set @ A),B:(set @ A)]: (((~ ((((member @ A) @ X) @ A3))) => ((~ ((((member @ A) @ X) @ B))) => (((((insert @ A) @ X) @ A3) = (((insert @ A) @ X) @ B)) = (A3 = B))))))).
% 3.01/1.52 thf(fact_33_Set_Oset__insert, axiom, (! [A:$tType,X:A,A3:(set @ A)]: (((((member @ A) @ X) @ A3) => (~ ((! [B4:(set @ A)]: (((A3 = (((insert @ A) @ X) @ B4)) => (((member @ A) @ X) @ B4)))))))))).
% 3.01/1.52 thf(fact_34_insertI2, axiom, (! [A:$tType,A2:A,B:(set @ A),B2:A]: (((((member @ A) @ A2) @ B) => (((member @ A) @ A2) @ (((insert @ A) @ B2) @ B)))))).
% 3.01/1.52 thf(fact_35_insertI1, axiom, (! [A:$tType,A2:A,B:(set @ A)]: ((((member @ A) @ A2) @ (((insert @ A) @ A2) @ B))))).
% 3.01/1.52 thf(fact_36_insertE, axiom, (! [A:$tType,A2:A,B2:A,A3:(set @ A)]: (((((member @ A) @ A2) @ (((insert @ A) @ B2) @ A3)) => ((A2 != B2) => (((member @ A) @ A2) @ A3)))))).
% 3.01/1.52 thf(fact_37_singleton__inject, axiom, (! [A:$tType,A2:A,B2:A]: ((((((insert @ A) @ A2) @ (bot_bot @ (set @ A))) = (((insert @ A) @ B2) @ (bot_bot @ (set @ A)))) => (A2 = B2))))).
% 3.01/1.52 thf(fact_38_insert__not__empty, axiom, (! [A:$tType,A2:A,A3:(set @ A)]: (((((insert @ A) @ A2) @ A3) != (bot_bot @ (set @ A)))))).
% 3.01/1.52 thf(fact_39_doubleton__eq__iff, axiom, (! [A:$tType,A2:A,B2:A,C:A,D2:A]: ((((((insert @ A) @ A2) @ (((insert @ A) @ B2) @ (bot_bot @ (set @ A)))) = (((insert @ A) @ C) @ (((insert @ A) @ D2) @ (bot_bot @ (set @ A))))) = (((A2 = C) & (B2 = D2)) | ((A2 = D2) & (B2 = C))))))).
% 3.01/1.52 thf(fact_40_singleton__iff, axiom, (! [A:$tType,B2:A,A2:A]: (((((member @ A) @ B2) @ (((insert @ A) @ A2) @ (bot_bot @ (set @ A)))) = (B2 = A2))))).
% 3.01/1.52 thf(fact_41_the__elem__eq, axiom, (! [A:$tType,X:A]: ((((the_elem @ A) @ (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) = X)))).
% 3.01/1.52 thf(fact_42_is__singletonI, axiom, (! [A:$tType,X:A]: (((is_singleton @ A) @ (((insert @ A) @ X) @ (bot_bot @ (set @ A))))))).
% 3.01/1.52 thf(fact_43_a11, axiom, ((ine @ p) @ (secrecy_kE @ key))).
% 3.01/1.52 thf(fact_44_TBtheorem3b, axiom, (! [P:secrecy_specID,M:(set @ secrecy_chanID),E:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: (((~ ((((ineM @ P) @ M) @ E))) => ((~ ((((ineM @ Q) @ M) @ E))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => (~ ((((ineM @ PQ) @ M) @ E)))))))))).
% 3.01/1.52 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 3.01/1.52 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A3:(set @ A)]: ((((collect @ A) @ (^ [X2:A]: ((((member @ A) @ X2) @ A3)))) = A3)))).
% 3.01/1.52 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((P @ X3) = (Q @ X3)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 3.01/1.52 thf(fact_48_ext, axiom, (! [B3:$tType,A:$tType,F:(A > B3),G:(A > B3)]: (((! [X3:A]: (((F @ X3) = (G @ X3)))) => (F = G))))).
% 3.01/1.52 thf(fact_49_TBtheorem1b, axiom, (! [PQ:secrecy_specID,M:(set @ secrecy_chanID),E:secrecy_Expression,P:secrecy_specID,Q:secrecy_specID]: (((((ineM @ PQ) @ M) @ E) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((((ineM @ P) @ M) @ E) | (((ineM @ Q) @ M) @ E)))))))).
% 3.01/1.52 thf(fact_50_a11ext, axiom, (((ine @ p) @ (secrecy_kE @ key)) | ((ine @ q) @ (secrecy_kE @ key)))).
% 3.01/1.52 thf(fact_51_Set_Ois__empty__def, axiom, (! [A:$tType]: (((is_empty @ A) = (^ [A4:(set @ A)]: ((A4 = (bot_bot @ (set @ A))))))))).
% 3.01/1.52 thf(fact_52_correctCompositionIn__prop1, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,X:secrecy_chanID]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((((member @ secrecy_chanID) @ X) @ (ins @ PQ)) => ((((member @ secrecy_chanID) @ X) @ (ins @ P)) | (((member @ secrecy_chanID) @ X) @ (ins @ Q))))))))).
% 3.01/1.52 thf(fact_53_correctCompositionIn__L2, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Ch:secrecy_chanID]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ PQ)) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ P)) | (((member @ secrecy_chanID) @ Ch) @ (ins @ Q))))))))).
% 3.01/1.52 thf(fact_54_is__singleton__def, axiom, (! [A:$tType]: (((is_singleton @ A) = (^ [A4:(set @ A)]: ((? [X2:A]: ((A4 = (((insert @ A) @ X2) @ (bot_bot @ (set @ A)))))))))))).
% 3.01/1.52 thf(fact_55_Expression_Oinject_I1_J, axiom, (! [X1:secrecy_Keys,Y1:secrecy_Keys]: ((((secrecy_kE @ X1) = (secrecy_kE @ Y1)) = (X1 = Y1))))).
% 3.01/1.52 thf(fact_56_not__ine__ineM, axiom, (! [P:secrecy_specID,E:secrecy_Expression,M:(set @ secrecy_chanID)]: (((~ (((ine @ P) @ E))) => (~ ((((ineM @ P) @ M) @ E))))))).
% 3.01/1.52 thf(fact_57_ineM__ine, axiom, (! [P:secrecy_specID,M:(set @ secrecy_chanID),E:secrecy_Expression]: (((((ineM @ P) @ M) @ E) => ((ine @ P) @ E))))).
% 3.01/1.52 thf(fact_58_not__know__k__not__ine, axiom, (! [A3:secrecy_specID,M2:secrecy_Keys]: (((~ (((knowle1437066798e_know @ A3) @ (secrecy_kKS @ M2)))) => (~ (((ine @ A3) @ (secrecy_kE @ M2)))))))).
% 3.01/1.52 thf(fact_59_is__singleton__the__elem, axiom, (! [A:$tType]: (((is_singleton @ A) = (^ [A4:(set @ A)]: ((A4 = (((insert @ A) @ ((the_elem @ A) @ A4)) @ (bot_bot @ (set @ A)))))))))).
% 3.01/1.52 thf(fact_60_is__singletonI_H, axiom, (! [A:$tType,A3:(set @ A)]: (((A3 != (bot_bot @ (set @ A))) => ((! [X3:A,Y:A]: (((((member @ A) @ X3) @ A3) => ((((member @ A) @ Y) @ A3) => (X3 = Y))))) => ((is_singleton @ A) @ A3)))))).
% 3.01/1.52 thf(fact_61_TBtheorem1a, axiom, (! [PQ:secrecy_specID,E:secrecy_Expression,P:secrecy_specID,Q:secrecy_specID]: ((((ine @ PQ) @ E) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => (((ine @ P) @ E) | ((ine @ Q) @ E)))))))).
% 3.01/1.52 thf(fact_62_TBtheorem3a, axiom, (! [P:secrecy_specID,E:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: (((~ (((ine @ P) @ E))) => ((~ (((ine @ Q) @ E))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => (~ (((ine @ PQ) @ E)))))))))).
% 3.01/1.52 thf(fact_63_is__singletonE, axiom, (! [A:$tType,A3:(set @ A)]: ((((is_singleton @ A) @ A3) => (~ ((! [X3:A]: ((A3 != (((insert @ A) @ X3) @ (bot_bot @ (set @ A)))))))))))).
% 3.01/1.52 thf(fact_64_bot__empty__eq, axiom, (! [A:$tType]: (((bot_bot @ (A > $o)) = (^ [X2:A]: ((((member @ A) @ X2) @ (bot_bot @ (set @ A))))))))).
% 3.01/1.52 thf(fact_65_Collect__empty__eq__bot, axiom, (! [A:$tType,P:(A > $o)]: (((((collect @ A) @ P) = (bot_bot @ (set @ A))) = (P = (bot_bot @ (A > $o))))))).
% 3.01/1.52 thf(fact_66_TBlemma3b, axiom, (! [P:secrecy_specID,M:(set @ secrecy_chanID),E:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID,Ch:secrecy_chanID]: (((~ ((((ineM @ P) @ M) @ E))) => ((~ ((((ineM @ Q) @ M) @ E))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((((member @ secrecy_chanID) @ Ch) @ M) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ PQ)) => (~ (((exprChannel @ Ch) @ E)))))))))))).
% 3.01/1.52 thf(fact_67_correctCompositionIn__L1, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Ch:secrecy_chanID]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((~ ((((member @ secrecy_chanID) @ Ch) @ (loc @ PQ)))) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ P)) => (((member @ secrecy_chanID) @ Ch) @ (ins @ PQ))))))))).
% 3.01/1.52 thf(fact_68_KS2Expression_Osimps_I1_J, axiom, (! [M2:secrecy_Keys]: (((secrec1016742679ession @ (secrecy_kKS @ M2)) = (secrecy_kE @ M2))))).
% 3.01/1.52 thf(fact_69_TBtheorem4a__empty, axiom, (! [P:secrecy_specID,E:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: (((((ine @ P) @ E) | ((ine @ Q) @ E)) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => (((loc @ PQ) = (bot_bot @ (set @ secrecy_chanID))) => ((ine @ PQ) @ E)))))))).
% 3.01/1.52 thf(fact_70_know_Osimps_I1_J, axiom, (! [A3:secrecy_specID,M2:secrecy_Keys]: ((((knowle1437066798e_know @ A3) @ (secrecy_kKS @ M2)) = (((ine @ A3) @ (secrecy_kE @ M2)) | (((member @ secrecy_KS) @ (secrecy_kKS @ M2)) @ (localSecrets @ A3))))))).
% 3.01/1.52 thf(fact_71_correctCompositionKS__exprChannel__k__P, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Key:secrecy_Keys,Ch:secrecy_chanID]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionKS @ PQ) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ Key)) @ (localSecrets @ PQ)))) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ P)) => (((exprChannel @ Ch) @ (secrecy_kE @ Key)) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ Key)) @ (specKeysSecrets @ PQ)))) => ((correctCompositionIn @ PQ) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ PQ)) & ((exprChannel @ Ch) @ (secrecy_kE @ Key))))))))))))).
% 3.01/1.52 thf(fact_72_LocalSecretsComposition__neg__loc__k, axiom, (! [Key:secrecy_Keys,P:secrecy_specID,Ch:secrecy_chanID]: (((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ Key)) @ (localSecrets @ P)))) => (((exprChannel @ Ch) @ (secrecy_kE @ Key)) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ Key)) @ (specKeysSecrets @ P)))) => (~ ((((member @ secrecy_chanID) @ Ch) @ (loc @ P)))))))))).
% 3.01/1.52 thf(fact_73_LocalSecretsComposition1, axiom, (! [Ls:secrecy_KS,P:secrecy_specID,PQ:secrecy_specID,Q:secrecy_specID]: (((((member @ secrecy_KS) @ Ls) @ (localSecrets @ P)) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => (((member @ secrecy_KS) @ Ls) @ (localSecrets @ PQ))))))).
% 3.01/1.52 thf(fact_74_LocalSecretsComposition__exprChannel__k, axiom, (! [X:secrecy_chanID,Keys:secrecy_Keys,P:secrecy_specID,Q:secrecy_specID]: ((((exprChannel @ X) @ (secrecy_kE @ Keys)) => ((~ (((ine @ P) @ (secrecy_kE @ Keys)))) => ((~ (((ine @ Q) @ (secrecy_kE @ Keys)))) => ((~ ((((member @ secrecy_chanID) @ X) @ (ins @ P)))) & (~ ((((member @ secrecy_chanID) @ X) @ (ins @ Q))))))))))).
% 3.01/1.52 thf(fact_75_ine__def, axiom, (ine = (^ [SP:secrecy_specID,E2:secrecy_Expression]: ((? [Ch2:secrecy_chanID]: (((((member @ secrecy_chanID) @ Ch2) @ (ins @ SP)) & ((exprChannel @ Ch2) @ E2)))))))).
% 3.01/1.52 thf(fact_76_ine__ins__neg1, axiom, (! [P:secrecy_specID,M2:secrecy_Expression,X:secrecy_chanID]: (((~ (((ine @ P) @ M2))) => (((exprChannel @ X) @ M2) => (~ ((((member @ secrecy_chanID) @ X) @ (ins @ P))))))))).
% 3.01/1.52 thf(fact_77_ineM__L1, axiom, (! [Ch:secrecy_chanID,M:(set @ secrecy_chanID),P:secrecy_specID,E:secrecy_Expression]: (((((member @ secrecy_chanID) @ Ch) @ M) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ P)) => (((exprChannel @ Ch) @ E) => (((ineM @ P) @ M) @ E))))))).
% 3.01/1.52 thf(fact_78_ineM__def, axiom, (ineM = (^ [SP:secrecy_specID,M3:(set @ secrecy_chanID),E2:secrecy_Expression]: ((? [Ch2:secrecy_chanID]: (((((member @ secrecy_chanID) @ Ch2) @ (ins @ SP)) & ((((member @ secrecy_chanID) @ Ch2) @ M3) & ((exprChannel @ Ch2) @ E2))))))))).
% 3.01/1.52 thf(fact_79_correctCompositionInLoc__exprChannel, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Ch:secrecy_chanID,M2:secrecy_Expression]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ P)) => (((exprChannel @ Ch) @ M2) => ((! [X3:secrecy_chanID]: (((((member @ secrecy_chanID) @ X3) @ (ins @ PQ)) => (~ (((exprChannel @ X3) @ M2)))))) => (((member @ secrecy_chanID) @ Ch) @ (loc @ PQ)))))))))).
% 3.01/1.52 thf(fact_80_TBtheorem4a__PQ, axiom, (! [P:secrecy_specID,E:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: (((((ine @ P) @ E) | ((ine @ Q) @ E)) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((? [Ch3:secrecy_chanID]: ((((((member @ secrecy_chanID) @ Ch3) @ (ins @ P)) | (((member @ secrecy_chanID) @ Ch3) @ (ins @ Q))) & (((exprChannel @ Ch3) @ E) & (~ ((((member @ secrecy_chanID) @ Ch3) @ (loc @ PQ)))))))) => ((ine @ PQ) @ E)))))))).
% 3.01/1.52 thf(fact_81_TBtheorem4a__P, axiom, (! [P:secrecy_specID,E:secrecy_Expression,PQ:secrecy_specID,Q:secrecy_specID]: ((((ine @ P) @ E) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((? [Ch3:secrecy_chanID]: (((((member @ secrecy_chanID) @ Ch3) @ (ins @ P)) & (((exprChannel @ Ch3) @ E) & (~ ((((member @ secrecy_chanID) @ Ch3) @ (loc @ PQ)))))))) => ((ine @ PQ) @ E)))))))).
% 3.01/1.52 thf(fact_82_TBtheorem4b__PQ, axiom, (! [P:secrecy_specID,M:(set @ secrecy_chanID),E:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: ((((((ineM @ P) @ M) @ E) | (((ineM @ Q) @ M) @ E)) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((? [Ch3:secrecy_chanID]: ((((((member @ secrecy_chanID) @ Ch3) @ (ins @ P)) | (((member @ secrecy_chanID) @ Ch3) @ (ins @ Q))) & ((((member @ secrecy_chanID) @ Ch3) @ M) & (((exprChannel @ Ch3) @ E) & (~ ((((member @ secrecy_chanID) @ Ch3) @ (loc @ PQ))))))))) => (((ineM @ PQ) @ M) @ E)))))))).
% 3.01/1.52 thf(fact_83_TBtheorem4b__P, axiom, (! [P:secrecy_specID,M:(set @ secrecy_chanID),E:secrecy_Expression,PQ:secrecy_specID,Q:secrecy_specID]: (((((ineM @ P) @ M) @ E) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((? [Ch3:secrecy_chanID]: (((((member @ secrecy_chanID) @ Ch3) @ (ins @ Q)) & (((exprChannel @ Ch3) @ E) & ((~ ((((member @ secrecy_chanID) @ Ch3) @ (loc @ PQ)))) & (((member @ secrecy_chanID) @ Ch3) @ M)))))) => (((ineM @ PQ) @ M) @ E)))))))).
% 3.01/1.52 thf(fact_84_correctCompositionKS__exprChannel__k__Qex, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Key:secrecy_Keys,Ch:secrecy_chanID]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionKS @ PQ) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ Key)) @ (localSecrets @ PQ)))) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ Q)) => (((exprChannel @ Ch) @ (secrecy_kE @ Key)) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ Key)) @ (specKeysSecrets @ PQ)))) => ((correctCompositionIn @ PQ) => (? [Ch4:secrecy_chanID]: (((((member @ secrecy_chanID) @ Ch4) @ (ins @ PQ)) & ((exprChannel @ Ch4) @ (secrecy_kE @ Key))))))))))))))).
% 3.01/1.52 thf(fact_85_correctCompositionKS__exprChannel__k__Pex, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Key:secrecy_Keys,Ch:secrecy_chanID]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionKS @ PQ) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ Key)) @ (localSecrets @ PQ)))) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ P)) => (((exprChannel @ Ch) @ (secrecy_kE @ Key)) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ Key)) @ (specKeysSecrets @ PQ)))) => ((correctCompositionIn @ PQ) => (? [Ch4:secrecy_chanID]: (((((member @ secrecy_chanID) @ Ch4) @ (ins @ PQ)) & ((exprChannel @ Ch4) @ (secrecy_kE @ Key))))))))))))))).
% 3.01/1.52 thf(fact_86_correctCompositionKS__exprChannel__k__Q, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Key:secrecy_Keys,Ch:secrecy_chanID]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionKS @ PQ) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ Key)) @ (localSecrets @ PQ)))) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ Q)) => (((exprChannel @ Ch) @ (secrecy_kE @ Key)) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ Key)) @ (specKeysSecrets @ PQ)))) => ((correctCompositionIn @ PQ) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ PQ)) & ((exprChannel @ Ch) @ (secrecy_kE @ Key))))))))))))).
% 3.01/1.52 thf(fact_87_TBtheorem4b__notP1, axiom, (! [P:secrecy_specID,M:(set @ secrecy_chanID),E:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: (((((ineM @ P) @ M) @ E) => ((~ ((((ineM @ Q) @ M) @ E))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((? [Ch3:secrecy_chanID]: (((((ine_ex1303305700Single @ P) @ Ch3) @ E) & ((((member @ secrecy_chanID) @ Ch3) @ M) & (((member @ secrecy_chanID) @ Ch3) @ (loc @ PQ)))))) => (~ ((((ineM @ PQ) @ M) @ E))))))))))).
% 3.01/1.52 thf(fact_88_TBtheorem4a__notP1, axiom, (! [P:secrecy_specID,E:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: ((((ine @ P) @ E) => ((~ (((ine @ Q) @ E))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((? [Ch3:secrecy_chanID]: (((((ine_ex1303305700Single @ P) @ Ch3) @ E) & (((member @ secrecy_chanID) @ Ch3) @ (loc @ PQ))))) => (~ (((ine @ PQ) @ E))))))))))).
% 3.01/1.52 thf(fact_89_LocalSecretsComposition__neg1__k, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Keys:secrecy_Keys]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc965049635ionLoc @ PQ) => ((~ (((ine @ P) @ (secrecy_kE @ Keys)))) => ((~ (((ine @ Q) @ (secrecy_kE @ Keys)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ Keys)) @ (localSecrets @ P)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ Keys)) @ (localSecrets @ Q)))) => (~ ((((member @ secrecy_KS) @ (secrecy_kKS @ Keys)) @ (localSecrets @ PQ))))))))))))).
% 3.01/1.52 thf(fact_90_LocalSecretsComposition__ine2__k, axiom, (! [K:secrecy_Keys,PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID]: (((((member @ secrecy_KS) @ (secrecy_kKS @ K)) @ (localSecrets @ PQ)) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc965049635ionLoc @ PQ) => ((~ (((ine @ P) @ (secrecy_kE @ K)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ K)) @ (localSecrets @ P)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ K)) @ (localSecrets @ Q)))) => ((ine @ Q) @ (secrecy_kE @ K))))))))))).
% 3.01/1.52 thf(fact_91_LocalSecretsComposition__ine1__k, axiom, (! [K:secrecy_Keys,PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID]: (((((member @ secrecy_KS) @ (secrecy_kKS @ K)) @ (localSecrets @ PQ)) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc965049635ionLoc @ PQ) => ((~ (((ine @ Q) @ (secrecy_kE @ K)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ K)) @ (localSecrets @ P)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ K)) @ (localSecrets @ Q)))) => ((ine @ P) @ (secrecy_kE @ K))))))))))).
% 3.01/1.52 thf(fact_92_TBtheorem4b__notPQ, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,ChSetP:(set @ secrecy_chanID),E:secrecy_Expression,ChSetQ:(set @ secrecy_chanID),M:(set @ secrecy_chanID)]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((((ine_exprChannelSet @ P) @ ChSetP) @ E) => ((((ine_exprChannelSet @ Q) @ ChSetQ) @ E) => ((! [X3:secrecy_chanID]: (((((member @ secrecy_chanID) @ X3) @ ChSetP) => (((member @ secrecy_chanID) @ X3) @ (loc @ PQ))))) => ((! [X3:secrecy_chanID]: (((((member @ secrecy_chanID) @ X3) @ ChSetQ) => (((member @ secrecy_chanID) @ X3) @ (loc @ PQ))))) => (~ ((((ineM @ PQ) @ M) @ E)))))))))))).
% 3.01/1.52 thf(fact_93_TBtheorem4b__notP2, axiom, (! [Q:secrecy_specID,M:(set @ secrecy_chanID),E:secrecy_Expression,PQ:secrecy_specID,P:secrecy_specID,ChSet:(set @ secrecy_chanID)]: (((~ ((((ineM @ Q) @ M) @ E))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((((ine_exprChannelSet @ P) @ ChSet) @ E) => ((! [X3:secrecy_chanID]: (((((member @ secrecy_chanID) @ X3) @ ChSet) => (((member @ secrecy_chanID) @ X3) @ (loc @ PQ))))) => (~ ((((ineM @ PQ) @ M) @ E))))))))))).
% 3.01/1.52 thf(fact_94_ine__exprChannelSingle__Set, axiom, (! [P:secrecy_specID,Ch:secrecy_chanID,E:secrecy_Expression]: (((((ine_ex1303305700Single @ P) @ Ch) @ E) => (((ine_exprChannelSet @ P) @ (((insert @ secrecy_chanID) @ Ch) @ (bot_bot @ (set @ secrecy_chanID)))) @ E))))).
% 3.01/1.52 thf(fact_95_ine__exprChannelSet__Single, axiom, (! [P:secrecy_specID,Ch:secrecy_chanID,E:secrecy_Expression]: (((((ine_exprChannelSet @ P) @ (((insert @ secrecy_chanID) @ Ch) @ (bot_bot @ (set @ secrecy_chanID)))) @ E) => (((ine_ex1303305700Single @ P) @ Ch) @ E))))).
% 3.01/1.52 thf(fact_96_ine__exprChannelSet__def, axiom, (ine_exprChannelSet = (^ [SP:secrecy_specID,ChSet2:(set @ secrecy_chanID),E2:secrecy_Expression]: (((! [X2:secrecy_chanID]: (((((member @ secrecy_chanID) @ X2) @ ChSet2) => ((((member @ secrecy_chanID) @ X2) @ (ins @ SP)) & ((exprChannel @ X2) @ E2))))) & (! [X2:secrecy_chanID]: ((((~ ((((member @ secrecy_chanID) @ X2) @ ChSet2))) & (((member @ secrecy_chanID) @ X2) @ (ins @ SP))) => (~ (((exprChannel @ X2) @ E2))))))))))).
% 3.01/1.52 thf(fact_97_ine__empty__exprChannelSet, axiom, (! [P:secrecy_specID,ChSet:(set @ secrecy_chanID),E:secrecy_Expression]: (((((ine_exprChannelSet @ P) @ ChSet) @ E) => ((ChSet = (bot_bot @ (set @ secrecy_chanID))) => (~ (((ine @ P) @ E)))))))).
% 3.01/1.52 thf(fact_98_ine__nonempty__exprChannelSet, axiom, (! [P:secrecy_specID,ChSet:(set @ secrecy_chanID),E:secrecy_Expression]: (((((ine_exprChannelSet @ P) @ ChSet) @ E) => ((ChSet != (bot_bot @ (set @ secrecy_chanID))) => ((ine @ P) @ E)))))).
% 3.01/1.52 thf(fact_99_ine__exprChannelSingle__def, axiom, (ine_ex1303305700Single = (^ [SP:secrecy_specID,Ch2:secrecy_chanID,E2:secrecy_Expression]: (((((member @ secrecy_chanID) @ Ch2) @ (ins @ SP)) & (((exprChannel @ Ch2) @ E2) & (! [X2:secrecy_chanID,T:nat]: ((((((member @ secrecy_chanID) @ X2) @ (ins @ SP)) & (X2 != Ch2)) => (~ (((exprChannel @ X2) @ E2)))))))))))).
% 3.01/1.52 thf(fact_100_TBtheorem4a__notP2, axiom, (! [Q:secrecy_specID,E:secrecy_Expression,PQ:secrecy_specID,P:secrecy_specID,ChSet:(set @ secrecy_chanID)]: (((~ (((ine @ Q) @ E))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((((ine_exprChannelSet @ P) @ ChSet) @ E) => ((! [X3:secrecy_chanID]: (((((member @ secrecy_chanID) @ X3) @ ChSet) => (((member @ secrecy_chanID) @ X3) @ (loc @ PQ))))) => (~ (((ine @ PQ) @ E))))))))))).
% 3.01/1.52 thf(fact_101_TBtheorem4a__notPQ, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,ChSetP:(set @ secrecy_chanID),E:secrecy_Expression,ChSetQ:(set @ secrecy_chanID)]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((((ine_exprChannelSet @ P) @ ChSetP) @ E) => ((((ine_exprChannelSet @ Q) @ ChSetQ) @ E) => ((! [X3:secrecy_chanID]: (((((member @ secrecy_chanID) @ X3) @ ChSetP) => (((member @ secrecy_chanID) @ X3) @ (loc @ PQ))))) => ((! [X3:secrecy_chanID]: (((((member @ secrecy_chanID) @ X3) @ ChSetQ) => (((member @ secrecy_chanID) @ X3) @ (loc @ PQ))))) => (~ (((ine @ PQ) @ E)))))))))))).
% 3.01/1.52 thf(fact_102_subcomponents__loc, axiom, (! [X:secrecy_specID]: (((correc965049635ionLoc @ X) => (((subcomponents @ X) = (bot_bot @ (set @ secrecy_specID))) => ((loc @ X) = (bot_bot @ (set @ secrecy_chanID)))))))).
% 3.01/1.52 thf(fact_103_LocalSecretsComposition__neg__k, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,M2:secrecy_Keys]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc965049635ionLoc @ PQ) => ((correctCompositionKS @ PQ) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ M2)) @ (specKeysSecrets @ P)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ M2)) @ (specKeysSecrets @ Q)))) => ((~ (((ine @ P) @ (secrecy_kE @ M2)))) => ((~ (((ine @ Q) @ (secrecy_kE @ M2)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ M2)) @ (((sup_sup @ (set @ secrecy_KS)) @ (localSecrets @ P)) @ (localSecrets @ Q))))) => (~ ((((member @ secrecy_KS) @ (secrecy_kKS @ M2)) @ (localSecrets @ PQ))))))))))))))).
% 3.01/1.52 thf(fact_104_correctCompositionKS__exprChannel__s__P, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Secret:secrecy_Secrets,Ch:secrecy_chanID]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionKS @ PQ) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ Secret)) @ (localSecrets @ PQ)))) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ P)) => (((exprChannel @ Ch) @ (secrecy_sE @ Secret)) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ Secret)) @ (specKeysSecrets @ PQ)))) => ((correctCompositionIn @ PQ) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ PQ)) & ((exprChannel @ Ch) @ (secrecy_sE @ Secret))))))))))))).
% 3.01/1.52 thf(fact_105_correctCompositionKS__exprChannel__s__Q, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Secret:secrecy_Secrets,Ch:secrecy_chanID]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionKS @ PQ) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ Secret)) @ (localSecrets @ PQ)))) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ Q)) => (((exprChannel @ Ch) @ (secrecy_sE @ Secret)) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ Secret)) @ (specKeysSecrets @ PQ)))) => ((correctCompositionIn @ PQ) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ PQ)) & ((exprChannel @ Ch) @ (secrecy_sE @ Secret))))))))))))).
% 3.01/1.52 thf(fact_106_correctCompositionKS__exprChannel__s__Pex, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Secret:secrecy_Secrets,Ch:secrecy_chanID]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionKS @ PQ) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ Secret)) @ (localSecrets @ PQ)))) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ P)) => (((exprChannel @ Ch) @ (secrecy_sE @ Secret)) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ Secret)) @ (specKeysSecrets @ PQ)))) => ((correctCompositionIn @ PQ) => (? [Ch4:secrecy_chanID]: (((((member @ secrecy_chanID) @ Ch4) @ (ins @ PQ)) & ((exprChannel @ Ch4) @ (secrecy_sE @ Secret))))))))))))))).
% 3.01/1.52 thf(fact_107_UnCI, axiom, (! [A:$tType,C:A,B:(set @ A),A3:(set @ A)]: ((((~ ((((member @ A) @ C) @ B))) => (((member @ A) @ C) @ A3)) => (((member @ A) @ C) @ (((sup_sup @ (set @ A)) @ A3) @ B)))))).
% 3.01/1.52 thf(fact_108_Un__iff, axiom, (! [A:$tType,C:A,A3:(set @ A),B:(set @ A)]: (((((member @ A) @ C) @ (((sup_sup @ (set @ A)) @ A3) @ B)) = ((((member @ A) @ C) @ A3) | (((member @ A) @ C) @ B)))))).
% 3.01/1.52 thf(fact_109_KS_Oinject_I2_J, axiom, (! [X22:secrecy_Secrets,Y22:secrecy_Secrets]: ((((secrecy_sKS @ X22) = (secrecy_sKS @ Y22)) = (X22 = Y22))))).
% 3.01/1.52 thf(fact_110_Expression_Oinject_I2_J, axiom, (! [X22:secrecy_Secrets,Y22:secrecy_Secrets]: ((((secrecy_sE @ X22) = (secrecy_sE @ Y22)) = (X22 = Y22))))).
% 3.01/1.52 thf(fact_111_Un__empty, axiom, (! [A:$tType,A3:(set @ A),B:(set @ A)]: ((((((sup_sup @ (set @ A)) @ A3) @ B) = (bot_bot @ (set @ A))) = ((A3 = (bot_bot @ (set @ A))) & (B = (bot_bot @ (set @ A)))))))).
% 3.01/1.52 thf(fact_112_Un__insert__right, axiom, (! [A:$tType,A3:(set @ A),A2:A,B:(set @ A)]: (((((sup_sup @ (set @ A)) @ A3) @ (((insert @ A) @ A2) @ B)) = (((insert @ A) @ A2) @ (((sup_sup @ (set @ A)) @ A3) @ B)))))).
% 3.01/1.52 thf(fact_113_Un__insert__left, axiom, (! [A:$tType,A2:A,B:(set @ A),C4:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((insert @ A) @ A2) @ B)) @ C4) = (((insert @ A) @ A2) @ (((sup_sup @ (set @ A)) @ B) @ C4)))))).
% 3.01/1.52 thf(fact_114_UnE, axiom, (! [A:$tType,C:A,A3:(set @ A),B:(set @ A)]: (((((member @ A) @ C) @ (((sup_sup @ (set @ A)) @ A3) @ B)) => ((~ ((((member @ A) @ C) @ A3))) => (((member @ A) @ C) @ B)))))).
% 3.01/1.52 thf(fact_115_UnI1, axiom, (! [A:$tType,C:A,A3:(set @ A),B:(set @ A)]: (((((member @ A) @ C) @ A3) => (((member @ A) @ C) @ (((sup_sup @ (set @ A)) @ A3) @ B)))))).
% 3.01/1.52 thf(fact_116_UnI2, axiom, (! [A:$tType,C:A,B:(set @ A),A3:(set @ A)]: (((((member @ A) @ C) @ B) => (((member @ A) @ C) @ (((sup_sup @ (set @ A)) @ A3) @ B)))))).
% 3.01/1.52 thf(fact_117_bex__Un, axiom, (! [A:$tType,A3:(set @ A),B:(set @ A),P:(A > $o)]: (((? [X2:A]: (((((member @ A) @ X2) @ (((sup_sup @ (set @ A)) @ A3) @ B)) & (P @ X2)))) = ((? [X2:A]: (((((member @ A) @ X2) @ A3) & (P @ X2)))) | (? [X2:A]: (((((member @ A) @ X2) @ B) & (P @ X2))))))))).
% 3.01/1.52 thf(fact_118_ball__Un, axiom, (! [A:$tType,A3:(set @ A),B:(set @ A),P:(A > $o)]: (((! [X2:A]: (((((member @ A) @ X2) @ (((sup_sup @ (set @ A)) @ A3) @ B)) => (P @ X2)))) = ((! [X2:A]: (((((member @ A) @ X2) @ A3) => (P @ X2)))) & (! [X2:A]: (((((member @ A) @ X2) @ B) => (P @ X2))))))))).
% 3.01/1.52 thf(fact_119_Un__assoc, axiom, (! [A:$tType,A3:(set @ A),B:(set @ A),C4:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A3) @ B)) @ C4) = (((sup_sup @ (set @ A)) @ A3) @ (((sup_sup @ (set @ A)) @ B) @ C4)))))).
% 3.01/1.52 thf(fact_120_Un__absorb, axiom, (! [A:$tType,A3:(set @ A)]: (((((sup_sup @ (set @ A)) @ A3) @ A3) = A3)))).
% 3.01/1.52 thf(fact_121_Un__commute, axiom, (! [A:$tType]: (((sup_sup @ (set @ A)) = (^ [A4:(set @ A),B5:(set @ A)]: ((((sup_sup @ (set @ A)) @ B5) @ A4))))))).
% 3.01/1.52 thf(fact_122_Un__left__absorb, axiom, (! [A:$tType,A3:(set @ A),B:(set @ A)]: (((((sup_sup @ (set @ A)) @ A3) @ (((sup_sup @ (set @ A)) @ A3) @ B)) = (((sup_sup @ (set @ A)) @ A3) @ B))))).
% 3.01/1.52 thf(fact_123_Un__left__commute, axiom, (! [A:$tType,A3:(set @ A),B:(set @ A),C4:(set @ A)]: (((((sup_sup @ (set @ A)) @ A3) @ (((sup_sup @ (set @ A)) @ B) @ C4)) = (((sup_sup @ (set @ A)) @ B) @ (((sup_sup @ (set @ A)) @ A3) @ C4)))))).
% 3.01/1.52 thf(fact_124_KS2Expression_Osimps_I2_J, axiom, (! [M2:secrecy_Secrets]: (((secrec1016742679ession @ (secrecy_sKS @ M2)) = (secrecy_sE @ M2))))).
% 3.01/1.52 thf(fact_125_Un__empty__right, axiom, (! [A:$tType,A3:(set @ A)]: (((((sup_sup @ (set @ A)) @ A3) @ (bot_bot @ (set @ A))) = A3)))).
% 3.01/1.52 thf(fact_126_Un__empty__left, axiom, (! [A:$tType,B:(set @ A)]: (((((sup_sup @ (set @ A)) @ (bot_bot @ (set @ A))) @ B) = B)))).
% 3.01/1.52 thf(fact_127_not__know__s__not__ine, axiom, (! [A3:secrecy_specID,M2:secrecy_Secrets]: (((~ (((knowle1437066798e_know @ A3) @ (secrecy_sKS @ M2)))) => (~ (((ine @ A3) @ (secrecy_sE @ M2)))))))).
% 3.01/1.52 thf(fact_128_KS_Oexhaust, axiom, (! [Y2:secrecy_KS]: (((! [X12:secrecy_Keys]: ((Y2 != (secrecy_kKS @ X12)))) => (~ ((! [X23:secrecy_Secrets]: ((Y2 != (secrecy_sKS @ X23)))))))))).
% 3.01/1.52 thf(fact_129_KS_Oinduct, axiom, (! [P:(secrecy_KS > $o),KS:secrecy_KS]: (((! [X3:secrecy_Keys]: ((P @ (secrecy_kKS @ X3)))) => ((! [X3:secrecy_Secrets]: ((P @ (secrecy_sKS @ X3)))) => (P @ KS)))))).
% 3.01/1.52 thf(fact_130_KS_Odistinct_I1_J, axiom, (! [X1:secrecy_Keys,X22:secrecy_Secrets]: (((secrecy_kKS @ X1) != (secrecy_sKS @ X22))))).
% 3.01/1.52 thf(fact_131_Expression_Odistinct_I1_J, axiom, (! [X1:secrecy_Keys,X22:secrecy_Secrets]: (((secrecy_kE @ X1) != (secrecy_sE @ X22))))).
% 3.01/1.52 thf(fact_132_know_Osimps_I2_J, axiom, (! [A3:secrecy_specID,M2:secrecy_Secrets]: ((((knowle1437066798e_know @ A3) @ (secrecy_sKS @ M2)) = (((ine @ A3) @ (secrecy_sE @ M2)) | (((member @ secrecy_KS) @ (secrecy_sKS @ M2)) @ (localSecrets @ A3))))))).
% 3.01/1.52 thf(fact_133_singleton__Un__iff, axiom, (! [A:$tType,X:A,A3:(set @ A),B:(set @ A)]: ((((((insert @ A) @ X) @ (bot_bot @ (set @ A))) = (((sup_sup @ (set @ A)) @ A3) @ B)) = (((A3 = (bot_bot @ (set @ A))) & (B = (((insert @ A) @ X) @ (bot_bot @ (set @ A))))) | (((A3 = (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) & (B = (bot_bot @ (set @ A)))) | ((A3 = (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) & (B = (((insert @ A) @ X) @ (bot_bot @ (set @ A))))))))))).
% 3.01/1.52 thf(fact_134_Un__singleton__iff, axiom, (! [A:$tType,A3:(set @ A),B:(set @ A),X:A]: ((((((sup_sup @ (set @ A)) @ A3) @ B) = (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) = (((A3 = (bot_bot @ (set @ A))) & (B = (((insert @ A) @ X) @ (bot_bot @ (set @ A))))) | (((A3 = (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) & (B = (bot_bot @ (set @ A)))) | ((A3 = (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) & (B = (((insert @ A) @ X) @ (bot_bot @ (set @ A))))))))))).
% 3.01/1.52 thf(fact_135_insert__is__Un, axiom, (! [A:$tType]: (((insert @ A) = (^ [A5:A]: (((sup_sup @ (set @ A)) @ (((insert @ A) @ A5) @ (bot_bot @ (set @ A)))))))))).
% 3.01/1.52 thf(fact_136_LocalSecretsComposition__neg__loc__s, axiom, (! [Secret:secrecy_Secrets,P:secrecy_specID,Ch:secrecy_chanID]: (((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ Secret)) @ (localSecrets @ P)))) => (((exprChannel @ Ch) @ (secrecy_sE @ Secret)) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ Secret)) @ (specKeysSecrets @ P)))) => (~ ((((member @ secrecy_chanID) @ Ch) @ (loc @ P)))))))))).
% 3.01/1.52 thf(fact_137_LocalSecretsComposition__neg__s, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,M2:secrecy_Secrets]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc965049635ionLoc @ PQ) => ((correctCompositionKS @ PQ) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ M2)) @ (specKeysSecrets @ P)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ M2)) @ (specKeysSecrets @ Q)))) => ((~ (((ine @ P) @ (secrecy_sE @ M2)))) => ((~ (((ine @ Q) @ (secrecy_sE @ M2)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ M2)) @ (((sup_sup @ (set @ secrecy_KS)) @ (localSecrets @ P)) @ (localSecrets @ Q))))) => (~ ((((member @ secrecy_KS) @ (secrecy_sKS @ M2)) @ (localSecrets @ PQ))))))))))))))).
% 3.01/1.52 thf(fact_138_LocalSecretsComposition__ine1__s, axiom, (! [S:secrecy_Secrets,PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID]: (((((member @ secrecy_KS) @ (secrecy_sKS @ S)) @ (localSecrets @ PQ)) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc965049635ionLoc @ PQ) => ((~ (((ine @ Q) @ (secrecy_sE @ S)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ S)) @ (localSecrets @ P)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ S)) @ (localSecrets @ Q)))) => ((ine @ P) @ (secrecy_sE @ S))))))))))).
% 3.01/1.52 thf(fact_139_LocalSecretsComposition__ine2__s, axiom, (! [S:secrecy_Secrets,PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID]: (((((member @ secrecy_KS) @ (secrecy_sKS @ S)) @ (localSecrets @ PQ)) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc965049635ionLoc @ PQ) => ((~ (((ine @ P) @ (secrecy_sE @ S)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ S)) @ (localSecrets @ P)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ S)) @ (localSecrets @ Q)))) => ((ine @ Q) @ (secrecy_sE @ S))))))))))).
% 3.01/1.52 thf(fact_140_LocalSecretsComposition__neg1__s, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,S:secrecy_Secrets]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc965049635ionLoc @ PQ) => ((~ (((ine @ P) @ (secrecy_sE @ S)))) => ((~ (((ine @ Q) @ (secrecy_sE @ S)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ S)) @ (localSecrets @ P)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ S)) @ (localSecrets @ Q)))) => (~ ((((member @ secrecy_KS) @ (secrecy_sKS @ S)) @ (localSecrets @ PQ))))))))))))).
% 3.01/1.52 thf(fact_141_LocalSecretsComposition__exprChannel__s, axiom, (! [X:secrecy_chanID,Secrets:secrecy_Secrets,P:secrecy_specID,Q:secrecy_specID]: ((((exprChannel @ X) @ (secrecy_sE @ Secrets)) => ((~ (((ine @ P) @ (secrecy_sE @ Secrets)))) => ((~ (((ine @ Q) @ (secrecy_sE @ Secrets)))) => ((~ ((((member @ secrecy_chanID) @ X) @ (ins @ P)))) & (~ ((((member @ secrecy_chanID) @ X) @ (ins @ Q))))))))))).
% 3.01/1.52 thf(fact_142_LocalSecretsComposition__neg, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Ks:secrecy_KS]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc965049635ionLoc @ PQ) => ((correctCompositionKS @ PQ) => ((~ ((((member @ secrecy_KS) @ Ks) @ (specKeysSecrets @ P)))) => ((~ ((((member @ secrecy_KS) @ Ks) @ (specKeysSecrets @ Q)))) => ((! [M4:secrecy_Keys]: (((Ks = (secrecy_kKS @ M4)) => ((~ (((ine @ P) @ (secrecy_kE @ M4)))) & (~ (((ine @ Q) @ (secrecy_kE @ M4)))))))) => ((! [M4:secrecy_Secrets]: (((Ks = (secrecy_sKS @ M4)) => ((~ (((ine @ P) @ (secrecy_sE @ M4)))) & (~ (((ine @ Q) @ (secrecy_sE @ M4)))))))) => ((~ ((((member @ secrecy_KS) @ Ks) @ (((sup_sup @ (set @ secrecy_KS)) @ (localSecrets @ P)) @ (localSecrets @ Q))))) => (~ ((((member @ secrecy_KS) @ Ks) @ (localSecrets @ PQ))))))))))))))).
% 3.01/1.52 thf(fact_143_LocalSecretsComposition__neg1, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Ks:secrecy_KS]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc965049635ionLoc @ PQ) => ((! [M4:secrecy_Keys]: (((Ks = (secrecy_kKS @ M4)) => ((~ (((ine @ P) @ (secrecy_kE @ M4)))) & (~ (((ine @ Q) @ (secrecy_kE @ M4)))))))) => ((! [M4:secrecy_Secrets]: (((Ks = (secrecy_sKS @ M4)) => ((~ (((ine @ P) @ (secrecy_sE @ M4)))) & (~ (((ine @ Q) @ (secrecy_sE @ M4)))))))) => ((~ ((((member @ secrecy_KS) @ Ks) @ (localSecrets @ P)))) => ((~ ((((member @ secrecy_KS) @ Ks) @ (localSecrets @ Q)))) => (~ ((((member @ secrecy_KS) @ Ks) @ (localSecrets @ PQ))))))))))))).
% 3.01/1.52 thf(fact_144_correctCompositionKS__exprChannel__s__Qex, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Secret:secrecy_Secrets,Ch:secrecy_chanID]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionKS @ PQ) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ Secret)) @ (localSecrets @ PQ)))) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ Q)) => (((exprChannel @ Ch) @ (secrecy_sE @ Secret)) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ Secret)) @ (specKeysSecrets @ PQ)))) => ((correctCompositionIn @ PQ) => (? [Ch4:secrecy_chanID]: (((((member @ secrecy_chanID) @ Ch4) @ (ins @ PQ)) & ((exprChannel @ Ch4) @ (secrecy_sE @ Secret))))))))))))))).
% 3.01/1.52 thf(fact_145_sup__bot_Oright__neutral, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [A2:A]: (((((sup_sup @ A) @ A2) @ (bot_bot @ A)) = A2))))))).
% 3.01/1.52 thf(fact_146_sup__bot_Oneutr__eq__iff, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [A2:A,B2:A]: ((((bot_bot @ A) = (((sup_sup @ A) @ A2) @ B2)) = ((A2 = (bot_bot @ A)) & (B2 = (bot_bot @ A)))))))))).
% 3.01/1.52 thf(fact_147_sup__bot_Oleft__neutral, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [A2:A]: (((((sup_sup @ A) @ (bot_bot @ A)) @ A2) = A2))))))).
% 3.01/1.52 thf(fact_148_sup__bot_Oeq__neutr__iff, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [A2:A,B2:A]: ((((((sup_sup @ A) @ A2) @ B2) = (bot_bot @ A)) = ((A2 = (bot_bot @ A)) & (B2 = (bot_bot @ A)))))))))).
% 3.01/1.52 thf(fact_149_sup__eq__bot__iff, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [X:A,Y2:A]: ((((((sup_sup @ A) @ X) @ Y2) = (bot_bot @ A)) = ((X = (bot_bot @ A)) & (Y2 = (bot_bot @ A)))))))))).
% 3.01/1.52 thf(fact_150_sup__bot__left, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [X:A]: (((((sup_sup @ A) @ (bot_bot @ A)) @ X) = X))))))).
% 3.01/1.52 thf(fact_151_sup__bot__right, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [X:A]: (((((sup_sup @ A) @ X) @ (bot_bot @ A)) = X))))))).
% 3.01/1.52 thf(fact_152_bot__eq__sup__iff, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [X:A,Y2:A]: ((((bot_bot @ A) = (((sup_sup @ A) @ X) @ Y2)) = ((X = (bot_bot @ A)) & (Y2 = (bot_bot @ A)))))))))).
% 3.01/1.52 thf(fact_153_ineM__Un1, axiom, (! [P:secrecy_specID,A3:(set @ secrecy_chanID),E:secrecy_Expression,B:(set @ secrecy_chanID)]: (((((ineM @ P) @ A3) @ E) => (((ineM @ P) @ (((sup_sup @ (set @ secrecy_chanID)) @ A3) @ B)) @ E))))).
% 3.01/1.52 thf(fact_154_locStream__def, axiom, (locStream = (^ [X2:secrecy_specID]: (((^ [Y3:(set @ secrecy_chanID),Z:(set @ secrecy_chanID)]: ((Y3 = Z))) @ (loc @ X2)))))).
% 3.01/1.52 thf(fact_155_inStream__def, axiom, (inStream = (^ [X2:secrecy_specID]: (((^ [Y3:(set @ secrecy_chanID),Z:(set @ secrecy_chanID)]: ((Y3 = Z))) @ (ins @ X2)))))).
% 3.01/1.52 thf(fact_156_notSpecKeysSecretsExpr__def, axiom, (notSpe1586871396tsExpr = (^ [P2:secrecy_specID,E3:(list @ secrecy_Expression)]: (((! [X2:secrecy_Keys]: (((((mem @ secrecy_Expression) @ (secrecy_kE @ X2)) @ E3) => (~ ((((member @ secrecy_KS) @ (secrecy_kKS @ X2)) @ (specKeysSecrets @ P2))))))) & (! [Y4:secrecy_Secrets]: (((((mem @ secrecy_Expression) @ (secrecy_sE @ Y4)) @ E3) => (~ ((((member @ secrecy_KS) @ (secrecy_sKS @ Y4)) @ (specKeysSecrets @ P2)))))))))))).
% 3.01/1.52 thf(fact_157_TBtheorem5a__empty, axiom, (! [P:secrecy_specID,E:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: (((((eout @ P) @ E) | ((eout @ Q) @ E)) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => (((loc @ PQ) = (bot_bot @ (set @ secrecy_chanID))) => ((eout @ PQ) @ E)))))))).
% 3.01/1.52 thf(fact_158_correctCompositionKS__subcomp4, axiom, (! [C4:secrecy_specID,X:secrecy_specID,Xa:secrecy_Secrets]: (((correctCompositionKS @ C4) => ((((member @ secrecy_specID) @ X) @ (subcomponents @ C4)) => ((((member @ secrecy_Secrets) @ Xa) @ (specSecrets @ X)) => (((member @ secrecy_Secrets) @ Xa) @ (specSecrets @ C4)))))))).
% 3.01/1.52 thf(fact_159_correctCompositionKS__subcomp3, axiom, (! [C4:secrecy_specID,X:secrecy_specID,Xa:secrecy_Keys]: (((correctCompositionKS @ C4) => ((((member @ secrecy_specID) @ X) @ (subcomponents @ C4)) => ((((member @ secrecy_Keys) @ Xa) @ (specKeys @ X)) => (((member @ secrecy_Keys) @ Xa) @ (specKeys @ C4)))))))).
% 3.01/1.52 thf(fact_160_TBtheorem2a, axiom, (! [PQ:secrecy_specID,E:secrecy_Expression,P:secrecy_specID,Q:secrecy_specID]: ((((eout @ PQ) @ E) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => (((eout @ P) @ E) | ((eout @ Q) @ E)))))))).
% 3.01/1.52 thf(fact_161_correctCompositionKS__subcomp1, axiom, (! [C4:secrecy_specID,X:secrecy_specID,Xa:secrecy_Keys]: (((correctCompositionKS @ C4) => ((((member @ secrecy_specID) @ X) @ (subcomponents @ C4)) => ((((member @ secrecy_Keys) @ Xa) @ (specKeys @ C4)) => (? [X3:secrecy_specID]: (((((member @ secrecy_specID) @ X3) @ (subcomponents @ C4)) & (((member @ secrecy_Keys) @ Xa) @ (specKeys @ X3))))))))))).
% 3.01/1.52 thf(fact_162_correctCompositionKS__subcomp2, axiom, (! [C4:secrecy_specID,X:secrecy_specID,Xa:secrecy_Secrets]: (((correctCompositionKS @ C4) => ((((member @ secrecy_specID) @ X) @ (subcomponents @ C4)) => ((((member @ secrecy_Secrets) @ Xa) @ (specSecrets @ C4)) => (? [X3:secrecy_specID]: (((((member @ secrecy_specID) @ X3) @ (subcomponents @ C4)) & (((member @ secrecy_Secrets) @ Xa) @ (specSecrets @ X3))))))))))).
% 3.01/1.52 thf(fact_163_TBtheorem5a__notP1, axiom, (! [P:secrecy_specID,E:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: ((((eout @ P) @ E) => ((~ (((eout @ Q) @ E))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => ((? [Ch3:secrecy_chanID]: (((((out_ex985543062Single @ P) @ Ch3) @ E) & (((member @ secrecy_chanID) @ Ch3) @ (loc @ PQ))))) => (~ (((eout @ PQ) @ E))))))))))).
% 3.01/1.52 thf(fact_164_TBtheorem5a__notP2, axiom, (! [Q:secrecy_specID,E:secrecy_Expression,PQ:secrecy_specID,P:secrecy_specID,ChSet:(set @ secrecy_chanID)]: (((~ (((eout @ Q) @ E))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => ((((out_exprChannelSet @ P) @ ChSet) @ E) => ((! [X3:secrecy_chanID]: (((((member @ secrecy_chanID) @ X3) @ ChSet) => (((member @ secrecy_chanID) @ X3) @ (loc @ PQ))))) => (~ (((eout @ PQ) @ E))))))))))).
% 3.01/1.52 thf(fact_165_TBtheorem5a__notPQ, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,ChSetP:(set @ secrecy_chanID),E:secrecy_Expression,ChSetQ:(set @ secrecy_chanID)]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => ((((out_exprChannelSet @ P) @ ChSetP) @ E) => ((((out_exprChannelSet @ Q) @ ChSetQ) @ E) => ((! [X3:secrecy_chanID]: (((((member @ secrecy_chanID) @ X3) @ ChSetP) => (((member @ secrecy_chanID) @ X3) @ (loc @ PQ))))) => ((! [X3:secrecy_chanID]: (((((member @ secrecy_chanID) @ X3) @ ChSetQ) => (((member @ secrecy_chanID) @ X3) @ (loc @ PQ))))) => (~ (((eout @ PQ) @ E)))))))))))).
% 3.01/1.52 thf(fact_166_out__exprChannelSet__Single, axiom, (! [P:secrecy_specID,Ch:secrecy_chanID,E:secrecy_Expression]: (((((out_exprChannelSet @ P) @ (((insert @ secrecy_chanID) @ Ch) @ (bot_bot @ (set @ secrecy_chanID)))) @ E) => (((out_ex985543062Single @ P) @ Ch) @ E))))).
% 3.01/1.52 thf(fact_167_out__exprChannelSingle__Set, axiom, (! [P:secrecy_specID,Ch:secrecy_chanID,E:secrecy_Expression]: (((((out_ex985543062Single @ P) @ Ch) @ E) => (((out_exprChannelSet @ P) @ (((insert @ secrecy_chanID) @ Ch) @ (bot_bot @ (set @ secrecy_chanID)))) @ E))))).
% 3.01/1.52 thf(fact_168_TBtheorem5b__notPQ, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,ChSetP:(set @ secrecy_chanID),E:secrecy_Expression,ChSetQ:(set @ secrecy_chanID),M:(set @ secrecy_chanID)]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => ((((out_exprChannelSet @ P) @ ChSetP) @ E) => ((((out_exprChannelSet @ Q) @ ChSetQ) @ E) => ((M = (((sup_sup @ (set @ secrecy_chanID)) @ ChSetP) @ ChSetQ)) => ((! [X3:secrecy_chanID]: (((((member @ secrecy_chanID) @ X3) @ ChSetP) => (((member @ secrecy_chanID) @ X3) @ (loc @ PQ))))) => ((! [X3:secrecy_chanID]: (((((member @ secrecy_chanID) @ X3) @ ChSetQ) => (((member @ secrecy_chanID) @ X3) @ (loc @ PQ))))) => (~ ((((eoutM @ PQ) @ M) @ E))))))))))))).
% 3.01/1.52 thf(fact_169_eout__know__s, axiom, (! [C4:secrecy_specID,M2:secrecy_Secrets]: ((((knowle1667810483orrect @ C4) @ (secrecy_sKS @ M2)) = (((eout @ C4) @ (secrecy_sE @ M2)) = ((((member @ secrecy_Secrets) @ M2) @ (specSecrets @ C4)) | ((knowle1437066798e_know @ C4) @ (secrecy_sKS @ M2)))))))).
% 3.01/1.52 thf(fact_170_not__know__s__not__eout, axiom, (! [M2:secrecy_Secrets,A3:secrecy_specID]: (((~ ((((member @ secrecy_Secrets) @ M2) @ (specSecrets @ A3)))) => ((~ (((knowle1437066798e_know @ A3) @ (secrecy_sKS @ M2)))) => (((knowle1667810483orrect @ A3) @ (secrecy_sKS @ M2)) => (~ (((eout @ A3) @ (secrecy_sE @ M2)))))))))).
% 3.01/1.52 thf(fact_171_not__eout__eoutM, axiom, (! [P:secrecy_specID,E:secrecy_Expression,M:(set @ secrecy_chanID)]: (((~ (((eout @ P) @ E))) => (~ ((((eoutM @ P) @ M) @ E))))))).
% 3.01/1.52 thf(fact_172_eoutM__eout, axiom, (! [P:secrecy_specID,M:(set @ secrecy_chanID),E:secrecy_Expression]: (((((eoutM @ P) @ M) @ E) => ((eout @ P) @ E))))).
% 3.01/1.52 thf(fact_173_TBtheorem2b, axiom, (! [PQ:secrecy_specID,M:(set @ secrecy_chanID),E:secrecy_Expression,P:secrecy_specID,Q:secrecy_specID]: (((((eoutM @ PQ) @ M) @ E) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => ((((eoutM @ P) @ M) @ E) | (((eoutM @ Q) @ M) @ E)))))))).
% 3.01/1.52 thf(fact_174_TBtheorem5b__notP2, axiom, (! [Q:secrecy_specID,M:(set @ secrecy_chanID),E:secrecy_Expression,PQ:secrecy_specID,P:secrecy_specID,ChSet:(set @ secrecy_chanID)]: (((~ ((((eoutM @ Q) @ M) @ E))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => ((((out_exprChannelSet @ P) @ ChSet) @ E) => ((! [X3:secrecy_chanID]: (((((member @ secrecy_chanID) @ X3) @ ChSet) => (((member @ secrecy_chanID) @ X3) @ (loc @ PQ))))) => (~ ((((eoutM @ PQ) @ M) @ E))))))))))).
% 3.01/1.52 thf(fact_175_TBtheorem5b__notP1, axiom, (! [P:secrecy_specID,M:(set @ secrecy_chanID),E:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: (((((eoutM @ P) @ M) @ E) => ((~ ((((eoutM @ Q) @ M) @ E))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => ((? [Ch3:secrecy_chanID]: (((((out_ex985543062Single @ P) @ Ch3) @ E) & ((((member @ secrecy_chanID) @ Ch3) @ M) & (((member @ secrecy_chanID) @ Ch3) @ (loc @ PQ)))))) => (~ ((((eoutM @ PQ) @ M) @ E))))))))))).
% 3.01/1.52 thf(fact_176_eout__know__k, axiom, (! [C4:secrecy_specID,M2:secrecy_Keys]: ((((knowle1667810483orrect @ C4) @ (secrecy_kKS @ M2)) = (((eout @ C4) @ (secrecy_kE @ M2)) = ((((member @ secrecy_Keys) @ M2) @ (specKeys @ C4)) | ((knowle1437066798e_know @ C4) @ (secrecy_kKS @ M2)))))))).
% 3.01/1.52 thf(fact_177_not__know__k__not__eout, axiom, (! [M2:secrecy_Keys,A3:secrecy_specID]: (((~ ((((member @ secrecy_Keys) @ M2) @ (specKeys @ A3)))) => ((~ (((knowle1437066798e_know @ A3) @ (secrecy_kKS @ M2)))) => (((knowle1667810483orrect @ A3) @ (secrecy_kKS @ M2)) => (~ (((eout @ A3) @ (secrecy_kE @ M2)))))))))).
% 3.01/1.52 thf(fact_178_eoutKnowCorrect__L1k, axiom, (! [C4:secrecy_specID,M2:secrecy_Keys]: ((((knowle1667810483orrect @ C4) @ (secrecy_kKS @ M2)) => (((eout @ C4) @ (secrecy_kE @ M2)) => ((((member @ secrecy_Keys) @ M2) @ (specKeys @ C4)) | ((knowle1437066798e_know @ C4) @ (secrecy_kKS @ M2)))))))).
% 3.01/1.52 thf(fact_179_eout__know__nonKS__k, axiom, (! [M2:secrecy_Keys,A3:secrecy_specID]: (((~ ((((member @ secrecy_Keys) @ M2) @ (specKeys @ A3)))) => (((eout @ A3) @ (secrecy_kE @ M2)) => (((knowle1667810483orrect @ A3) @ (secrecy_kKS @ M2)) => ((knowle1437066798e_know @ A3) @ (secrecy_kKS @ M2)))))))).
% 3.01/1.52 thf(fact_180_eout__know__nonKS__s, axiom, (! [M2:secrecy_Secrets,A3:secrecy_specID]: (((~ ((((member @ secrecy_Secrets) @ M2) @ (specSecrets @ A3)))) => (((eout @ A3) @ (secrecy_sE @ M2)) => (((knowle1667810483orrect @ A3) @ (secrecy_sKS @ M2)) => ((knowle1437066798e_know @ A3) @ (secrecy_sKS @ M2)))))))).
% 3.01/1.52 thf(fact_181_eoutKnowCorrect__L1s, axiom, (! [C4:secrecy_specID,M2:secrecy_Secrets]: ((((knowle1667810483orrect @ C4) @ (secrecy_sKS @ M2)) => (((eout @ C4) @ (secrecy_sE @ M2)) => ((((member @ secrecy_Secrets) @ M2) @ (specSecrets @ C4)) | ((knowle1437066798e_know @ C4) @ (secrecy_sKS @ M2)))))))).
% 3.01/1.52 thf(fact_182_TBtheorem5b__PQ, axiom, (! [P:secrecy_specID,M:(set @ secrecy_chanID),E:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: ((((((eoutM @ P) @ M) @ E) | (((eoutM @ Q) @ M) @ E)) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => ((? [Ch3:secrecy_chanID]: ((((((member @ secrecy_chanID) @ Ch3) @ (out @ P)) | (((member @ secrecy_chanID) @ Ch3) @ (out @ Q))) & ((((member @ secrecy_chanID) @ Ch3) @ M) & (((exprChannel @ Ch3) @ E) & (~ ((((member @ secrecy_chanID) @ Ch3) @ (loc @ PQ))))))))) => (((eoutM @ PQ) @ M) @ E)))))))).
% 3.01/1.52 thf(fact_183_TBtheore54b__P, axiom, (! [P:secrecy_specID,M:(set @ secrecy_chanID),E:secrecy_Expression,PQ:secrecy_specID,Q:secrecy_specID]: (((((eoutM @ P) @ M) @ E) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => ((? [Ch3:secrecy_chanID]: (((((member @ secrecy_chanID) @ Ch3) @ (out @ Q)) & (((exprChannel @ Ch3) @ E) & ((~ ((((member @ secrecy_chanID) @ Ch3) @ (loc @ PQ)))) & (((member @ secrecy_chanID) @ Ch3) @ M)))))) => (((eoutM @ PQ) @ M) @ E)))))))).
% 3.01/1.52 thf(fact_184_TBtheorem5a__PQ, axiom, (! [P:secrecy_specID,E:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: (((((eout @ P) @ E) | ((eout @ Q) @ E)) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => ((? [Ch3:secrecy_chanID]: ((((((member @ secrecy_chanID) @ Ch3) @ (out @ P)) | (((member @ secrecy_chanID) @ Ch3) @ (out @ Q))) & (((exprChannel @ Ch3) @ E) & (~ ((((member @ secrecy_chanID) @ Ch3) @ (loc @ PQ)))))))) => ((eout @ PQ) @ E)))))))).
% 3.01/1.52 thf(fact_185_eout__def, axiom, (eout = (^ [SP:secrecy_specID,E2:secrecy_Expression]: ((? [Ch2:secrecy_chanID]: (((((member @ secrecy_chanID) @ Ch2) @ (out @ SP)) & ((exprChannel @ Ch2) @ E2)))))))).
% 3.01/1.52 thf(fact_186_eoutM__def, axiom, (eoutM = (^ [SP:secrecy_specID,M3:(set @ secrecy_chanID),E2:secrecy_Expression]: ((? [Ch2:secrecy_chanID]: (((((member @ secrecy_chanID) @ Ch2) @ (out @ SP)) & ((((member @ secrecy_chanID) @ Ch2) @ M3) & ((exprChannel @ Ch2) @ E2))))))))).
% 3.01/1.52 thf(fact_187_out__exprChannelSet__def, axiom, (out_exprChannelSet = (^ [SP:secrecy_specID,ChSet2:(set @ secrecy_chanID),E2:secrecy_Expression]: (((! [X2:secrecy_chanID]: (((((member @ secrecy_chanID) @ X2) @ ChSet2) => ((((member @ secrecy_chanID) @ X2) @ (out @ SP)) & ((exprChannel @ X2) @ E2))))) & (! [X2:secrecy_chanID]: ((((~ ((((member @ secrecy_chanID) @ X2) @ ChSet2))) & (((member @ secrecy_chanID) @ X2) @ (out @ SP))) => (~ (((exprChannel @ X2) @ E2))))))))))).
% 3.01/1.52 thf(fact_188_out__exprChannelSingle__def, axiom, (out_ex985543062Single = (^ [SP:secrecy_specID,Ch2:secrecy_chanID,E2:secrecy_Expression]: (((((member @ secrecy_chanID) @ Ch2) @ (out @ SP)) & (((exprChannel @ Ch2) @ E2) & (! [X2:secrecy_chanID,T:nat]: ((((((member @ secrecy_chanID) @ X2) @ (out @ SP)) & (X2 != Ch2)) => (~ (((exprChannel @ X2) @ E2)))))))))))).
% 3.01/1.52 thf(fact_189_correctCompositionOut__prop1, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,X:secrecy_chanID]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => ((((member @ secrecy_chanID) @ X) @ (out @ PQ)) => ((((member @ secrecy_chanID) @ X) @ (out @ P)) | (((member @ secrecy_chanID) @ X) @ (out @ Q))))))))).
% 3.01/1.52 thf(fact_190_TBtheorem45a__P, axiom, (! [P:secrecy_specID,E:secrecy_Expression,PQ:secrecy_specID,Q:secrecy_specID]: ((((eout @ P) @ E) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => ((? [Ch3:secrecy_chanID]: (((((member @ secrecy_chanID) @ Ch3) @ (out @ P)) & (((exprChannel @ Ch3) @ E) & (~ ((((member @ secrecy_chanID) @ Ch3) @ (loc @ PQ)))))))) => ((eout @ PQ) @ E)))))))).
% 3.01/1.52 thf(fact_191_adv__not__know2, axiom, (! [P:secrecy_specID,A3:secrecy_specID,M2:secrecy_Secrets]: (((((ord_less_eq @ (set @ secrecy_chanID)) @ (out @ P)) @ (ins @ A3)) => ((~ (((knowle1437066798e_know @ A3) @ (secrecy_sKS @ M2)))) => (~ (((eout @ P) @ (secrecy_sE @ M2))))))))).
% 3.01/1.52 thf(fact_192_adv__not__know1, axiom, (! [P:secrecy_specID,A3:secrecy_specID,M2:secrecy_Keys]: (((((ord_less_eq @ (set @ secrecy_chanID)) @ (out @ P)) @ (ins @ A3)) => ((~ (((knowle1437066798e_know @ A3) @ (secrecy_kKS @ M2)))) => (~ (((eout @ P) @ (secrecy_kE @ M2))))))))).
% 3.01/1.52 thf(fact_193_correctCompositionKeys__subcomp1, axiom, (! [C4:secrecy_specID,X:secrecy_specID,Xb:secrecy_Keys]: (((correc17873122onKeys @ C4) => ((((member @ secrecy_specID) @ X) @ (subcomponents @ C4)) => ((((member @ secrecy_Keys) @ Xb) @ (specKeys @ C4)) => (? [X3:secrecy_specID]: (((((member @ secrecy_specID) @ X3) @ (subcomponents @ C4)) & (((member @ secrecy_Keys) @ Xb) @ (specKeys @ X3))))))))))).
% 3.01/1.52 thf(fact_194_order__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A]: ((((ord_less_eq @ A) @ X) @ X))))))).
% 3.01/1.52 thf(fact_195_subset__antisym, axiom, (! [A:$tType,A3:(set @ A),B:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ B) => ((((ord_less_eq @ (set @ A)) @ B) @ A3) => (A3 = B)))))).
% 3.01/1.52 thf(fact_196_subsetI, axiom, (! [A:$tType,A3:(set @ A),B:(set @ A)]: (((! [X3:A]: (((((member @ A) @ X3) @ A3) => (((member @ A) @ X3) @ B)))) => (((ord_less_eq @ (set @ A)) @ A3) @ B))))).
% 3.01/1.52 thf(fact_197_empty__subsetI, axiom, (! [A:$tType,A3:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ (bot_bot @ (set @ A))) @ A3)))).
% 3.01/1.52 thf(fact_198_subset__empty, axiom, (! [A:$tType,A3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ (bot_bot @ (set @ A))) = (A3 = (bot_bot @ (set @ A))))))).
% 3.01/1.52 thf(fact_199_insert__subset, axiom, (! [A:$tType,X:A,A3:(set @ A),B:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ (((insert @ A) @ X) @ A3)) @ B) = ((((member @ A) @ X) @ B) & (((ord_less_eq @ (set @ A)) @ A3) @ B)))))).
% 3.01/1.52 thf(fact_200_Un__subset__iff, axiom, (! [A:$tType,A3:(set @ A),B:(set @ A),C4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A3) @ B)) @ C4) = ((((ord_less_eq @ (set @ A)) @ A3) @ C4) & (((ord_less_eq @ (set @ A)) @ B) @ C4)))))).
% 3.01/1.52 thf(fact_201_singleton__insert__inj__eq, axiom, (! [A:$tType,B2:A,A2:A,A3:(set @ A)]: ((((((insert @ A) @ B2) @ (bot_bot @ (set @ A))) = (((insert @ A) @ A2) @ A3)) = ((A2 = B2) & (((ord_less_eq @ (set @ A)) @ A3) @ (((insert @ A) @ B2) @ (bot_bot @ (set @ A))))))))).
% 3.01/1.52 thf(fact_202_singleton__insert__inj__eq_H, axiom, (! [A:$tType,A2:A,A3:(set @ A),B2:A]: ((((((insert @ A) @ A2) @ A3) = (((insert @ A) @ B2) @ (bot_bot @ (set @ A)))) = ((A2 = B2) & (((ord_less_eq @ (set @ A)) @ A3) @ (((insert @ A) @ B2) @ (bot_bot @ (set @ A))))))))).
% 3.01/1.52 thf(fact_203_subset__singleton__iff, axiom, (! [A:$tType,X4:(set @ A),A2:A]: (((((ord_less_eq @ (set @ A)) @ X4) @ (((insert @ A) @ A2) @ (bot_bot @ (set @ A)))) = ((X4 = (bot_bot @ (set @ A))) | (X4 = (((insert @ A) @ A2) @ (bot_bot @ (set @ A))))))))).
% 3.01/1.52 thf(fact_204_subset__singletonD, axiom, (! [A:$tType,A3:(set @ A),X:A]: (((((ord_less_eq @ (set @ A)) @ A3) @ (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) => ((A3 = (bot_bot @ (set @ A))) | (A3 = (((insert @ A) @ X) @ (bot_bot @ (set @ A))))))))).
% 3.01/1.52 thf(fact_205_subset__Un__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A4:(set @ A),B5:(set @ A)]: (((((sup_sup @ (set @ A)) @ A4) @ B5) = B5))))))).
% 3.01/1.52 thf(fact_206_subset__UnE, axiom, (! [A:$tType,C4:(set @ A),A3:(set @ A),B:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ C4) @ (((sup_sup @ (set @ A)) @ A3) @ B)) => (~ ((! [A6:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A6) @ A3) => (! [B6:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ B6) @ B) => (C4 != (((sup_sup @ (set @ A)) @ A6) @ B6)))))))))))))).
% 3.01/1.52 thf(fact_207_Un__absorb2, axiom, (! [A:$tType,B:(set @ A),A3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ B) @ A3) => ((((sup_sup @ (set @ A)) @ A3) @ B) = A3))))).
% 3.01/1.52 thf(fact_208_Un__absorb1, axiom, (! [A:$tType,A3:(set @ A),B:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ B) => ((((sup_sup @ (set @ A)) @ A3) @ B) = B))))).
% 3.01/1.52 thf(fact_209_Un__upper2, axiom, (! [A:$tType,B:(set @ A),A3:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ B) @ (((sup_sup @ (set @ A)) @ A3) @ B))))).
% 3.01/1.52 thf(fact_210_Un__upper1, axiom, (! [A:$tType,A3:(set @ A),B:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A3) @ (((sup_sup @ (set @ A)) @ A3) @ B))))).
% 3.01/1.52 thf(fact_211_Un__least, axiom, (! [A:$tType,A3:(set @ A),C4:(set @ A),B:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ C4) => ((((ord_less_eq @ (set @ A)) @ B) @ C4) => (((ord_less_eq @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A3) @ B)) @ C4)))))).
% 3.01/1.52 thf(fact_212_Un__mono, axiom, (! [A:$tType,A3:(set @ A),C4:(set @ A),B:(set @ A),D3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ C4) => ((((ord_less_eq @ (set @ A)) @ B) @ D3) => (((ord_less_eq @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A3) @ B)) @ (((sup_sup @ (set @ A)) @ C4) @ D3))))))).
% 3.01/1.52 thf(fact_213_bot_Oextremum__uniqueI, axiom, (! [A:$tType]: (((order_bot @ A) => (! [A2:A]: (((((ord_less_eq @ A) @ A2) @ (bot_bot @ A)) => (A2 = (bot_bot @ A))))))))).
% 3.01/1.52 thf(fact_214_bot_Oextremum__unique, axiom, (! [A:$tType]: (((order_bot @ A) => (! [A2:A]: (((((ord_less_eq @ A) @ A2) @ (bot_bot @ A)) = (A2 = (bot_bot @ A))))))))).
% 3.01/1.52 thf(fact_215_bot_Oextremum, axiom, (! [A:$tType]: (((order_bot @ A) => (! [A2:A]: ((((ord_less_eq @ A) @ (bot_bot @ A)) @ A2))))))).
% 3.01/1.52 thf(fact_216_subset__insertI2, axiom, (! [A:$tType,A3:(set @ A),B:(set @ A),B2:A]: (((((ord_less_eq @ (set @ A)) @ A3) @ B) => (((ord_less_eq @ (set @ A)) @ A3) @ (((insert @ A) @ B2) @ B)))))).
% 3.01/1.52 thf(fact_217_subset__insertI, axiom, (! [A:$tType,B:(set @ A),A2:A]: ((((ord_less_eq @ (set @ A)) @ B) @ (((insert @ A) @ A2) @ B))))).
% 3.01/1.52 thf(fact_218_subset__insert, axiom, (! [A:$tType,X:A,A3:(set @ A),B:(set @ A)]: (((~ ((((member @ A) @ X) @ A3))) => ((((ord_less_eq @ (set @ A)) @ A3) @ (((insert @ A) @ X) @ B)) = (((ord_less_eq @ (set @ A)) @ A3) @ B)))))).
% 3.01/1.52 thf(fact_219_insert__mono, axiom, (! [A:$tType,C4:(set @ A),D3:(set @ A),A2:A]: (((((ord_less_eq @ (set @ A)) @ C4) @ D3) => (((ord_less_eq @ (set @ A)) @ (((insert @ A) @ A2) @ C4)) @ (((insert @ A) @ A2) @ D3)))))).
% 3.01/1.52 thf(fact_220_dual__order_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ A2) @ B2) => (A2 = B2))))))))).
% 3.01/1.52 thf(fact_221_dual__order_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y3:A,Z:A]: ((Y3 = Z))) = (^ [A5:A,B7:A]: (((((ord_less_eq @ A) @ B7) @ A5) & (((ord_less_eq @ A) @ A5) @ B7))))))))).
% 3.01/1.52 thf(fact_222_dual__order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A,C:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ C) @ B2) => (((ord_less_eq @ A) @ C) @ A2))))))))).
% 3.01/1.52 thf(fact_223_linorder__wlog, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > (A > $o)),A2:A,B2:A]: (((! [A7:A,B8:A]: (((((ord_less_eq @ A) @ A7) @ B8) => ((P @ A7) @ B8)))) => ((! [A7:A,B8:A]: ((((P @ B8) @ A7) => ((P @ A7) @ B8)))) => ((P @ A2) @ B2))))))))).
% 3.01/1.52 thf(fact_224_dual__order_Orefl, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A]: ((((ord_less_eq @ A) @ A2) @ A2))))))).
% 3.01/1.52 thf(fact_225_order__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y2:A,Z2:A]: (((((ord_less_eq @ A) @ X) @ Y2) => ((((ord_less_eq @ A) @ Y2) @ Z2) => (((ord_less_eq @ A) @ X) @ Z2))))))))).
% 3.01/1.52 thf(fact_226_order__class_Oorder_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ B2) @ A2) => (A2 = B2))))))))).
% 3.01/1.52 thf(fact_227_ord__le__eq__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B2:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((B2 = C) => (((ord_less_eq @ A) @ A2) @ C))))))))).
% 3.01/1.52 thf(fact_228_ord__eq__le__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B2:A,C:A]: (((A2 = B2) => ((((ord_less_eq @ A) @ B2) @ C) => (((ord_less_eq @ A) @ A2) @ C))))))))).
% 3.01/1.52 thf(fact_229_order__class_Oorder_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y3:A,Z:A]: ((Y3 = Z))) = (^ [A5:A,B7:A]: (((((ord_less_eq @ A) @ A5) @ B7) & (((ord_less_eq @ A) @ B7) @ A5))))))))).
% 3.01/1.52 thf(fact_230_antisym__conv, axiom, (! [A:$tType]: (((order @ A) => (! [Y2:A,X:A]: (((((ord_less_eq @ A) @ Y2) @ X) => ((((ord_less_eq @ A) @ X) @ Y2) = (X = Y2))))))))).
% 3.01/1.52 thf(fact_231_le__cases3, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y2:A,Z2:A]: ((((((ord_less_eq @ A) @ X) @ Y2) => (~ ((((ord_less_eq @ A) @ Y2) @ Z2)))) => (((((ord_less_eq @ A) @ Y2) @ X) => (~ ((((ord_less_eq @ A) @ X) @ Z2)))) => (((((ord_less_eq @ A) @ X) @ Z2) => (~ ((((ord_less_eq @ A) @ Z2) @ Y2)))) => (((((ord_less_eq @ A) @ Z2) @ Y2) => (~ ((((ord_less_eq @ A) @ Y2) @ X)))) => (((((ord_less_eq @ A) @ Y2) @ Z2) => (~ ((((ord_less_eq @ A) @ Z2) @ X)))) => (~ (((((ord_less_eq @ A) @ Z2) @ X) => (~ ((((ord_less_eq @ A) @ X) @ Y2))))))))))))))))).
% 3.01/1.52 thf(fact_232_order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ B2) @ C) => (((ord_less_eq @ A) @ A2) @ C))))))))).
% 3.01/1.52 thf(fact_233_le__cases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y2:A]: (((~ ((((ord_less_eq @ A) @ X) @ Y2))) => (((ord_less_eq @ A) @ Y2) @ X)))))))).
% 3.01/1.52 thf(fact_234_eq__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y2:A]: (((X = Y2) => (((ord_less_eq @ A) @ X) @ Y2)))))))).
% 3.01/1.52 thf(fact_235_linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y2:A]: (((((ord_less_eq @ A) @ X) @ Y2) | (((ord_less_eq @ A) @ Y2) @ X)))))))).
% 3.01/1.52 thf(fact_236_antisym, axiom, (! [A:$tType]: (((order @ A) => (! [X:A,Y2:A]: (((((ord_less_eq @ A) @ X) @ Y2) => ((((ord_less_eq @ A) @ Y2) @ X) => (X = Y2))))))))).
% 3.01/1.52 thf(fact_237_eq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y3:A,Z:A]: ((Y3 = Z))) = (^ [X2:A,Y4:A]: (((((ord_less_eq @ A) @ X2) @ Y4) & (((ord_less_eq @ A) @ Y4) @ X2))))))))).
% 3.01/1.52 thf(fact_238_ord__le__eq__subst, axiom, (! [A:$tType,B3:$tType]: ((((ord @ B3) & (ord @ A)) => (! [A2:A,B2:A,F:(A > B3),C:B3]: (((((ord_less_eq @ A) @ A2) @ B2) => (((F @ B2) = C) => ((! [X3:A,Y:A]: (((((ord_less_eq @ A) @ X3) @ Y) => (((ord_less_eq @ B3) @ (F @ X3)) @ (F @ Y))))) => (((ord_less_eq @ B3) @ (F @ A2)) @ C)))))))))).
% 3.01/1.52 thf(fact_239_ord__eq__le__subst, axiom, (! [A:$tType,B3:$tType]: ((((ord @ B3) & (ord @ A)) => (! [A2:A,F:(B3 > A),B2:B3,C:B3]: (((A2 = (F @ B2)) => ((((ord_less_eq @ B3) @ B2) @ C) => ((! [X3:B3,Y:B3]: (((((ord_less_eq @ B3) @ X3) @ Y) => (((ord_less_eq @ A) @ (F @ X3)) @ (F @ Y))))) => (((ord_less_eq @ A) @ A2) @ (F @ C))))))))))).
% 3.01/1.52 thf(fact_240_order__subst2, axiom, (! [A:$tType,C2:$tType]: ((((order @ C2) & (order @ A)) => (! [A2:A,B2:A,F:(A > C2),C:C2]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ C2) @ (F @ B2)) @ C) => ((! [X3:A,Y:A]: (((((ord_less_eq @ A) @ X3) @ Y) => (((ord_less_eq @ C2) @ (F @ X3)) @ (F @ Y))))) => (((ord_less_eq @ C2) @ (F @ A2)) @ C)))))))))).
% 3.01/1.52 thf(fact_241_order__subst1, axiom, (! [A:$tType,B3:$tType]: ((((order @ B3) & (order @ A)) => (! [A2:A,F:(B3 > A),B2:B3,C:B3]: (((((ord_less_eq @ A) @ A2) @ (F @ B2)) => ((((ord_less_eq @ B3) @ B2) @ C) => ((! [X3:B3,Y:B3]: (((((ord_less_eq @ B3) @ X3) @ Y) => (((ord_less_eq @ A) @ (F @ X3)) @ (F @ Y))))) => (((ord_less_eq @ A) @ A2) @ (F @ C))))))))))).
% 3.01/1.52 thf(fact_242_Collect__mono__iff, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)) = (! [X2:A]: (((P @ X2) => (Q @ X2)))))))).
% 3.01/1.52 thf(fact_243_le__fun__def, axiom, (! [B3:$tType,A:$tType]: (((ord @ B3) => ((ord_less_eq @ (A > B3)) = (^ [F2:(A > B3),G2:(A > B3)]: ((! [X2:A]: ((((ord_less_eq @ B3) @ (F2 @ X2)) @ (G2 @ X2))))))))))).
% 3.01/1.52 thf(fact_244_set__eq__subset, axiom, (! [A:$tType]: (((^ [Y3:(set @ A),Z:(set @ A)]: ((Y3 = Z))) = (^ [A4:(set @ A),B5:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ B5) & (((ord_less_eq @ (set @ A)) @ B5) @ A4)))))))).
% 3.01/1.52 thf(fact_245_le__funI, axiom, (! [B3:$tType,A:$tType]: (((ord @ B3) => (! [F:(A > B3),G:(A > B3)]: (((! [X3:A]: ((((ord_less_eq @ B3) @ (F @ X3)) @ (G @ X3)))) => (((ord_less_eq @ (A > B3)) @ F) @ G)))))))).
% 3.01/1.52 thf(fact_246_le__funE, axiom, (! [B3:$tType,A:$tType]: (((ord @ B3) => (! [F:(A > B3),G:(A > B3),X:A]: (((((ord_less_eq @ (A > B3)) @ F) @ G) => (((ord_less_eq @ B3) @ (F @ X)) @ (G @ X))))))))).
% 3.01/1.52 thf(fact_247_le__funD, axiom, (! [B3:$tType,A:$tType]: (((ord @ B3) => (! [F:(A > B3),G:(A > B3),X:A]: (((((ord_less_eq @ (A > B3)) @ F) @ G) => (((ord_less_eq @ B3) @ (F @ X)) @ (G @ X))))))))).
% 3.01/1.52 thf(fact_248_subset__trans, axiom, (! [A:$tType,A3:(set @ A),B:(set @ A),C4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A3) @ B) => ((((ord_less_eq @ (set @ A)) @ B) @ C4) => (((ord_less_eq @ (set @ A)) @ A3) @ C4)))))).
% 3.01/1.52 thf(fact_249_Collect__mono, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((P @ X3) => (Q @ X3)))) => (((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)))))).
% 3.01/1.52 thf(fact_250_subset__refl, axiom, (! [A:$tType,A3:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A3) @ A3)))).
% 3.01/1.52 thf(fact_251_subset__iff, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A4:(set @ A),B5:(set @ A)]: ((! [T:A]: (((((member @ A) @ T) @ A4) => (((member @ A) @ T) @ B5)))))))))).
% 3.01/1.52 thf(fact_252_equalityD2, axiom, (! [A:$tType,A3:(set @ A),B:(set @ A)]: (((A3 = B) => (((ord_less_eq @ (set @ A)) @ B) @ A3))))).
% 3.01/1.52 thf(fact_253_equalityD1, axiom, (! [A:$tType,A3:(set @ A),B:(set @ A)]: (((A3 = B) => (((ord_less_eq @ (set @ A)) @ A3) @ B))))).
% 3.01/1.52 thf(fact_254_subset__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A4:(set @ A),B5:(set @ A)]: ((! [X2:A]: (((((member @ A) @ X2) @ A4) => (((member @ A) @ X2) @ B5)))))))))).
% 3.01/1.52 thf(fact_255_equalityE, axiom, (! [A:$tType,A3:(set @ A),B:(set @ A)]: (((A3 = B) => (~ (((((ord_less_eq @ (set @ A)) @ A3) @ B) => (~ ((((ord_less_eq @ (set @ A)) @ B) @ A3)))))))))).
% 3.01/1.52 thf(tcon_HOL_Obool___Lattices_Obounded__lattice, axiom, (bounded_lattice @ $o)).
% 3.01/1.52 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1, axiom, (! [A8:$tType]: ((bounded_lattice @ (set @ A8))))).
% 3.01/1.52 thf(tcon_fun___Lattices_Obounded__lattice_2, axiom, (! [A8:$tType,A9:$tType]: (((bounded_lattice @ A9) => (bounded_lattice @ (A8 > A9)))))).
% 3.01/1.52 thf(tcon_fun___Lattices_Obounded__semilattice__sup__bot, axiom, (! [A8:$tType,A9:$tType]: (((bounded_lattice @ A9) => (bounde1808546759up_bot @ (A8 > A9)))))).
% 3.01/1.52 thf(tcon_fun___Orderings_Oorder__bot, axiom, (! [A8:$tType,A9:$tType]: (((order_bot @ A9) => (order_bot @ (A8 > A9)))))).
% 3.01/1.52 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A8:$tType,A9:$tType]: (((preorder @ A9) => (preorder @ (A8 > A9)))))).
% 3.01/1.52 thf(tcon_fun___Orderings_Oorder, axiom, (! [A8:$tType,A9:$tType]: (((order @ A9) => (order @ (A8 > A9)))))).
% 3.01/1.52 thf(tcon_fun___Orderings_Oord, axiom, (! [A8:$tType,A9:$tType]: (((ord @ A9) => (ord @ (A8 > A9)))))).
% 3.01/1.52 thf(tcon_fun___Orderings_Obot, axiom, (! [A8:$tType,A9:$tType]: (((bot @ A9) => (bot @ (A8 > A9)))))).
% 3.01/1.52 thf(tcon_Nat_Onat___Orderings_Oorder__bot_3, axiom, (order_bot @ nat)).
% 3.01/1.52 thf(tcon_Nat_Onat___Orderings_Opreorder_4, axiom, (preorder @ nat)).
% 3.01/1.52 thf(tcon_Nat_Onat___Orderings_Olinorder, axiom, (linorder @ nat)).
% 3.01/1.52 thf(tcon_Nat_Onat___Orderings_Oorder_5, axiom, (order @ nat)).
% 3.01/1.52 thf(tcon_Nat_Onat___Orderings_Oord_6, axiom, (ord @ nat)).
% 3.01/1.52 thf(tcon_Nat_Onat___Orderings_Obot_7, axiom, (bot @ nat)).
% 3.01/1.52 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_8, axiom, (! [A8:$tType]: ((bounde1808546759up_bot @ (set @ A8))))).
% 3.01/1.52 thf(tcon_Set_Oset___Orderings_Oorder__bot_9, axiom, (! [A8:$tType]: ((order_bot @ (set @ A8))))).
% 3.01/1.52 thf(tcon_Set_Oset___Orderings_Opreorder_10, axiom, (! [A8:$tType]: ((preorder @ (set @ A8))))).
% 3.01/1.52 thf(tcon_Set_Oset___Orderings_Oorder_11, axiom, (! [A8:$tType]: ((order @ (set @ A8))))).
% 3.01/1.52 thf(tcon_Set_Oset___Orderings_Oord_12, axiom, (! [A8:$tType]: ((ord @ (set @ A8))))).
% 3.01/1.52 thf(tcon_Set_Oset___Orderings_Obot_13, axiom, (! [A8:$tType]: ((bot @ (set @ A8))))).
% 3.01/1.52 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_14, axiom, (bounde1808546759up_bot @ $o)).
% 3.01/1.52 thf(tcon_HOL_Obool___Orderings_Oorder__bot_15, axiom, (order_bot @ $o)).
% 3.01/1.52 thf(tcon_HOL_Obool___Orderings_Opreorder_16, axiom, (preorder @ $o)).
% 3.01/1.52 thf(tcon_HOL_Obool___Orderings_Olinorder_17, axiom, (linorder @ $o)).
% 3.01/1.52 thf(tcon_HOL_Obool___Orderings_Oorder_18, axiom, (order @ $o)).
% 3.01/1.52 thf(tcon_HOL_Obool___Orderings_Oord_19, axiom, (ord @ $o)).
% 3.01/1.52 thf(tcon_HOL_Obool___Orderings_Obot_20, axiom, (bot @ $o)).
% 3.01/1.52 thf(conj_0, conjecture, (~ ((((member @ secrecy_KS) @ m) @ (specKeysSecrets @ pq))))).
% 3.01/1.52 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.OaDn1w6qtU/DTF2DTF5010.p
% 3.01/1.52 ------------------------
% 3.01/1.55 ---- Cleaned THF ---
% 3.01/1.55 thf(ty_t_Secrecy__types_OExpression,type,
% 3.01/1.55 secrecy_Expression: $tType ).
% 3.01/1.55
% 3.01/1.55 thf(ty_t_Secrecy__types_OSecrets,type,
% 3.01/1.55 secrecy_Secrets: $tType ).
% 3.01/1.55
% 3.01/1.55 thf(ty_t_Secrecy__types_OspecID,type,
% 3.01/1.55 secrecy_specID: $tType ).
% 3.01/1.55
% 3.01/1.55 thf(ty_t_Secrecy__types_OchanID,type,
% 3.01/1.55 secrecy_chanID: $tType ).
% 3.01/1.55
% 3.01/1.55 thf(ty_t_Secrecy__types_OKeys,type,
% 3.01/1.55 secrecy_Keys: $tType ).
% 3.01/1.55
% 3.01/1.55 thf(ty_t_Secrecy__types_OKS,type,
% 3.01/1.55 secrecy_KS: $tType ).
% 3.01/1.55
% 3.01/1.55 thf(ty_t_List_Olist,type,
% 3.01/1.55 list: $tType > $tType ).
% 3.01/1.55
% 3.01/1.55 thf(ty_t_Set_Oset,type,
% 3.01/1.55 set: $tType > $tType ).
% 3.01/1.55
% 3.01/1.55 thf(ty_t_Nat_Onat,type,
% 3.01/1.55 nat: $tType ).
% 3.01/1.55
% 3.01/1.55 thf(sy_cl_Lattices_Obounded__lattice,type,
% 3.01/1.55 bounded_lattice:
% 3.01/1.55 !>[A: $tType] : $o ).
% 3.01/1.55
% 3.01/1.55 thf(sy_cl_HOL_Otype,type,
% 3.01/1.55 type:
% 3.01/1.55 !>[A: $tType] : $o ).
% 3.01/1.55
% 3.01/1.55 thf(sy_cl_Orderings_Obot,type,
% 3.01/1.55 bot:
% 3.01/1.55 !>[A: $tType] : $o ).
% 3.01/1.55
% 3.01/1.55 thf(sy_cl_Orderings_Oord,type,
% 3.01/1.55 ord:
% 3.01/1.55 !>[A: $tType] : $o ).
% 3.01/1.55
% 3.01/1.55 thf(sy_cl_Orderings_Oorder,type,
% 3.01/1.55 order:
% 3.01/1.55 !>[A: $tType] : $o ).
% 3.01/1.55
% 3.01/1.55 thf(sy_cl_Orderings_Olinorder,type,
% 3.01/1.55 linorder:
% 3.01/1.55 !>[A: $tType] : $o ).
% 3.01/1.55
% 3.01/1.55 thf(sy_cl_Orderings_Opreorder,type,
% 3.01/1.55 preorder:
% 3.01/1.55 !>[A: $tType] : $o ).
% 3.01/1.55
% 3.01/1.55 thf(sy_cl_Orderings_Oorder__bot,type,
% 3.01/1.55 order_bot:
% 3.01/1.55 !>[A: $tType] : $o ).
% 3.01/1.55
% 3.01/1.55 thf(sy_cl_Lattices_Obounded__semilattice__sup__bot,type,
% 3.01/1.55 bounde1808546759up_bot:
% 3.01/1.55 !>[A: $tType] : $o ).
% 3.01/1.55
% 3.01/1.55 thf(sy_c_CompLocalSecrets_OLocalSecrets,type,
% 3.01/1.55 localSecrets: secrecy_specID > ( set @ secrecy_KS ) ).
% 3.01/1.55
% 3.01/1.55 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__khazhniute_OeoutKnowCorrect,type,
% 3.01/1.55 knowle1667810483orrect: secrecy_specID > secrecy_KS > $o ).
% 3.01/1.55
% 3.01/1.55 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__khazhniute_Oknow,type,
% 3.01/1.55 knowle1437066798e_know: secrecy_specID > secrecy_KS > $o ).
% 3.01/1.55
% 3.01/1.55 thf(sy_c_Lattices_Osup__class_Osup,type,
% 3.01/1.55 sup_sup:
% 3.01/1.55 !>[A: $tType] : ( A > A > A ) ).
% 3.01/1.55
% 3.01/1.55 thf(sy_c_ListExtras_Omem,type,
% 3.01/1.55 mem:
% 3.01/1.55 !>[A: $tType] : ( A > ( list @ A ) > $o ) ).
% 3.01/1.55
% 3.01/1.55 thf(sy_c_Orderings_Obot__class_Obot,type,
% 3.01/1.55 bot_bot:
% 3.01/1.55 !>[A: $tType] : A ).
% 3.01/1.55
% 3.01/1.55 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 3.01/1.55 ord_less_eq:
% 3.01/1.55 !>[A: $tType] : ( A > A > $o ) ).
% 3.01/1.55
% 3.01/1.55 thf(sy_c_Secrecy_OcorrectCompositionKS,type,
% 3.01/1.55 correctCompositionKS: secrecy_specID > $o ).
% 3.01/1.55
% 3.01/1.55 thf(sy_c_Secrecy_OcorrectCompositionKeys,type,
% 3.01/1.55 correc17873122onKeys: secrecy_specID > $o ).
% 3.01/1.55
% 3.01/1.55 thf(sy_c_Secrecy_Oeout,type,
% 3.01/1.55 eout: secrecy_specID > secrecy_Expression > $o ).
% 3.01/1.55
% 3.01/1.55 thf(sy_c_Secrecy_OeoutM,type,
% 3.01/1.55 eoutM: secrecy_specID > ( set @ secrecy_chanID ) > secrecy_Expression > $o ).
% 3.01/1.55
% 3.01/1.55 thf(sy_c_Secrecy_OexprChannel,type,
% 3.01/1.55 exprChannel: secrecy_chanID > secrecy_Expression > $o ).
% 3.01/1.55
% 3.01/1.55 thf(sy_c_Secrecy_Oine,type,
% 3.01/1.55 ine: secrecy_specID > secrecy_Expression > $o ).
% 3.01/1.55
% 3.01/1.55 thf(sy_c_Secrecy_OineM,type,
% 3.01/1.55 ineM: secrecy_specID > ( set @ secrecy_chanID ) > secrecy_Expression > $o ).
% 3.01/1.55
% 3.01/1.55 thf(sy_c_Secrecy_Oine__exprChannelSet,type,
% 3.01/1.55 ine_exprChannelSet: secrecy_specID > ( set @ secrecy_chanID ) > secrecy_Expression > $o ).
% 3.01/1.55
% 3.01/1.55 thf(sy_c_Secrecy_Oine__exprChannelSingle,type,
% 3.01/1.55 ine_ex1303305700Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
% 3.01/1.55
% 3.01/1.55 thf(sy_c_Secrecy_OnotSpecKeysSecretsExpr,type,
% 3.01/1.55 notSpe1586871396tsExpr: secrecy_specID > ( list @ secrecy_Expression ) > $o ).
% 3.01/1.55
% 3.01/1.55 thf(sy_c_Secrecy_Oout__exprChannelSet,type,
% 3.01/1.55 out_exprChannelSet: secrecy_specID > ( set @ secrecy_chanID ) > secrecy_Expression > $o ).
% 3.01/1.55
% 3.01/1.55 thf(sy_c_Secrecy_Oout__exprChannelSingle,type,
% 3.01/1.55 out_ex985543062Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
% 3.01/1.55
% 3.01/1.55 thf(sy_c_Secrecy_OspecKeys,type,
% 3.01/1.55 specKeys: secrecy_specID > ( set @ secrecy_Keys ) ).
% 3.01/1.55
% 3.01/1.55 thf(sy_c_Secrecy_OspecKeysSecrets,type,
% 3.01/1.55 specKeysSecrets: secrecy_specID > ( set @ secrecy_KS ) ).
% 3.01/1.55
% 3.01/1.55 thf(sy_c_Secrecy_OspecSecrets,type,
% 3.01/1.55 specSecrets: secrecy_specID > ( set @ secrecy_Secrets ) ).
% 3.01/1.55
% 3.01/1.55 thf(sy_c_Secrecy__types_OExpression_OkE,type,
% 3.01/1.55 secrecy_kE: secrecy_Keys > secrecy_Expression ).
% 3.01/1.55
% 3.01/1.55 thf(sy_c_Secrecy__types_OExpression_OsE,type,
% 3.01/1.55 secrecy_sE: secrecy_Secrets > secrecy_Expression ).
% 3.01/1.55
% 3.01/1.55 thf(sy_c_Secrecy__types_OKS2Expression,type,
% 3.01/1.55 secrec1016742679ession: secrecy_KS > secrecy_Expression ).
% 3.01/1.55
% 3.01/1.55 thf(sy_c_Secrecy__types_OKS_OkKS,type,
% 3.01/1.55 secrecy_kKS: secrecy_Keys > secrecy_KS ).
% 3.01/1.55
% 3.01/1.55 thf(sy_c_Secrecy__types_OKS_OsKS,type,
% 3.01/1.55 secrecy_sKS: secrecy_Secrets > secrecy_KS ).
% 3.01/1.55
% 3.01/1.55 thf(sy_c_Set_OCollect,type,
% 3.01/1.55 collect:
% 3.01/1.55 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(sy_c_Set_Oinsert,type,
% 3.01/1.55 insert:
% 3.01/1.55 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(sy_c_Set_Ois__empty,type,
% 3.01/1.55 is_empty:
% 3.01/1.55 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 3.01/1.55
% 3.01/1.55 thf(sy_c_Set_Ois__singleton,type,
% 3.01/1.55 is_singleton:
% 3.01/1.55 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 3.01/1.55
% 3.01/1.55 thf(sy_c_Set_Othe__elem,type,
% 3.01/1.55 the_elem:
% 3.01/1.55 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 3.01/1.55
% 3.01/1.55 thf(sy_c_inout_OcorrectCompositionIn,type,
% 3.01/1.55 correctCompositionIn: secrecy_specID > $o ).
% 3.01/1.55
% 3.01/1.55 thf(sy_c_inout_OcorrectCompositionLoc,type,
% 3.01/1.55 correc965049635ionLoc: secrecy_specID > $o ).
% 3.01/1.55
% 3.01/1.55 thf(sy_c_inout_OcorrectCompositionOut,type,
% 3.01/1.55 correc990227761ionOut: secrecy_specID > $o ).
% 3.01/1.55
% 3.01/1.55 thf(sy_c_inout_OinStream,type,
% 3.01/1.55 inStream: secrecy_specID > ( set @ secrecy_chanID ) > $o ).
% 3.01/1.55
% 3.01/1.55 thf(sy_c_inout_Oins,type,
% 3.01/1.55 ins: secrecy_specID > ( set @ secrecy_chanID ) ).
% 3.01/1.55
% 3.01/1.55 thf(sy_c_inout_Oloc,type,
% 3.01/1.55 loc: secrecy_specID > ( set @ secrecy_chanID ) ).
% 3.01/1.55
% 3.01/1.55 thf(sy_c_inout_OlocStream,type,
% 3.01/1.55 locStream: secrecy_specID > ( set @ secrecy_chanID ) > $o ).
% 3.01/1.55
% 3.01/1.55 thf(sy_c_inout_Oout,type,
% 3.01/1.55 out: secrecy_specID > ( set @ secrecy_chanID ) ).
% 3.01/1.55
% 3.01/1.55 thf(sy_c_inout_Osubcomponents,type,
% 3.01/1.55 subcomponents: secrecy_specID > ( set @ secrecy_specID ) ).
% 3.01/1.55
% 3.01/1.55 thf(sy_c_member,type,
% 3.01/1.55 member:
% 3.01/1.55 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 3.01/1.55
% 3.01/1.55 thf(sy_v_P,type,
% 3.01/1.55 p: secrecy_specID ).
% 3.01/1.55
% 3.01/1.55 thf(sy_v_PQ,type,
% 3.01/1.55 pq: secrecy_specID ).
% 3.01/1.55
% 3.01/1.55 thf(sy_v_Q,type,
% 3.01/1.55 q: secrecy_specID ).
% 3.01/1.55
% 3.01/1.55 thf(sy_v_key____,type,
% 3.01/1.55 key: secrecy_Keys ).
% 3.01/1.55
% 3.01/1.55 thf(sy_v_m,type,
% 3.01/1.55 m: secrecy_KS ).
% 3.01/1.55
% 3.01/1.55 thf(fact_0_cCompKS,axiom,
% 3.01/1.55 correctCompositionKS @ pq ).
% 3.01/1.55
% 3.01/1.55 thf(fact_1_notKSQ,axiom,
% 3.01/1.55 ~ ( member @ secrecy_KS @ m @ ( specKeysSecrets @ q ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_2_notKSP,axiom,
% 3.01/1.55 ~ ( member @ secrecy_KS @ m @ ( specKeysSecrets @ p ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_3_subPQ,axiom,
% 3.01/1.55 ( ( subcomponents @ pq )
% 3.01/1.55 = ( insert @ secrecy_specID @ p @ ( insert @ secrecy_specID @ q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_4_cCompI,axiom,
% 3.01/1.55 correctCompositionIn @ pq ).
% 3.01/1.55
% 3.01/1.55 thf(fact_5_assms_I3_J,axiom,
% 3.01/1.55 knowle1437066798e_know @ p @ m ).
% 3.01/1.55
% 3.01/1.55 thf(fact_6_a1,axiom,
% 3.01/1.55 ( m
% 3.01/1.55 = ( secrecy_kKS @ key ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_7_correctCompositionKS__PQ,axiom,
% 3.01/1.55 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 3.01/1.55 ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correctCompositionKS @ PQ )
% 3.01/1.55 => ( ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 3.01/1.55 => ( ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 3.01/1.55 | ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_8_correctCompositionKS__neg1,axiom,
% 3.01/1.55 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 3.01/1.55 ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correctCompositionKS @ PQ )
% 3.01/1.55 => ( ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 3.01/1.55 => ( ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) )
% 3.01/1.55 => ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_9_correctCompositionKS__negP,axiom,
% 3.01/1.55 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 3.01/1.55 ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correctCompositionKS @ PQ )
% 3.01/1.55 => ( ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 3.01/1.55 => ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ P ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_10_correctCompositionKS__negQ,axiom,
% 3.01/1.55 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 3.01/1.55 ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correctCompositionKS @ PQ )
% 3.01/1.55 => ( ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 3.01/1.55 => ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_11_singletonI,axiom,
% 3.01/1.55 ! [A: $tType,A2: A] : ( member @ A @ A2 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_12_KS_Oinject_I1_J,axiom,
% 3.01/1.55 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 3.01/1.55 ( ( ( secrecy_kKS @ X1 )
% 3.01/1.55 = ( secrecy_kKS @ Y1 ) )
% 3.01/1.55 = ( X1 = Y1 ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_13_insertCI,axiom,
% 3.01/1.55 ! [A: $tType,A2: A,B: set @ A,B2: A] :
% 3.01/1.55 ( ( ~ ( member @ A @ A2 @ B )
% 3.01/1.55 => ( A2 = B2 ) )
% 3.01/1.55 => ( member @ A @ A2 @ ( insert @ A @ B2 @ B ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_14_insert__iff,axiom,
% 3.01/1.55 ! [A: $tType,A2: A,B2: A,A3: set @ A] :
% 3.01/1.55 ( ( member @ A @ A2 @ ( insert @ A @ B2 @ A3 ) )
% 3.01/1.55 = ( ( A2 = B2 )
% 3.01/1.55 | ( member @ A @ A2 @ A3 ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_15_insert__absorb2,axiom,
% 3.01/1.55 ! [A: $tType,X: A,A3: set @ A] :
% 3.01/1.55 ( ( insert @ A @ X @ ( insert @ A @ X @ A3 ) )
% 3.01/1.55 = ( insert @ A @ X @ A3 ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_16_empty__iff,axiom,
% 3.01/1.55 ! [A: $tType,C: A] :
% 3.01/1.55 ~ ( member @ A @ C @ ( bot_bot @ ( set @ A ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_17_all__not__in__conv,axiom,
% 3.01/1.55 ! [A: $tType,A3: set @ A] :
% 3.01/1.55 ( ( ! [X2: A] :
% 3.01/1.55 ~ ( member @ A @ X2 @ A3 ) )
% 3.01/1.55 = ( A3
% 3.01/1.55 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_18_Collect__empty__eq,axiom,
% 3.01/1.55 ! [A: $tType,P: A > $o] :
% 3.01/1.55 ( ( ( collect @ A @ P )
% 3.01/1.55 = ( bot_bot @ ( set @ A ) ) )
% 3.01/1.55 = ( ! [X2: A] :
% 3.01/1.55 ~ ( P @ X2 ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_19_empty__Collect__eq,axiom,
% 3.01/1.55 ! [A: $tType,P: A > $o] :
% 3.01/1.55 ( ( ( bot_bot @ ( set @ A ) )
% 3.01/1.55 = ( collect @ A @ P ) )
% 3.01/1.55 = ( ! [X2: A] :
% 3.01/1.55 ~ ( P @ X2 ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_20_bot__apply,axiom,
% 3.01/1.55 ! [C2: $tType,D: $tType] :
% 3.01/1.55 ( ( bot @ C2 )
% 3.01/1.55 => ( ( bot_bot @ ( D > C2 ) )
% 3.01/1.55 = ( ^ [X2: D] : ( bot_bot @ C2 ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_21_singletonD,axiom,
% 3.01/1.55 ! [A: $tType,B2: A,A2: A] :
% 3.01/1.55 ( ( member @ A @ B2 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 3.01/1.55 => ( B2 = A2 ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_22_bot__set__def,axiom,
% 3.01/1.55 ! [A: $tType] :
% 3.01/1.55 ( ( bot_bot @ ( set @ A ) )
% 3.01/1.55 = ( collect @ A @ ( bot_bot @ ( A > $o ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_23_bot__fun__def,axiom,
% 3.01/1.55 ! [B3: $tType,A: $tType] :
% 3.01/1.55 ( ( bot @ B3 )
% 3.01/1.55 => ( ( bot_bot @ ( A > B3 ) )
% 3.01/1.55 = ( ^ [X2: A] : ( bot_bot @ B3 ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_24_ex__in__conv,axiom,
% 3.01/1.55 ! [A: $tType,A3: set @ A] :
% 3.01/1.55 ( ( ? [X2: A] : ( member @ A @ X2 @ A3 ) )
% 3.01/1.55 = ( A3
% 3.01/1.55 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_25_equals0I,axiom,
% 3.01/1.55 ! [A: $tType,A3: set @ A] :
% 3.01/1.55 ( ! [Y: A] :
% 3.01/1.55 ~ ( member @ A @ Y @ A3 )
% 3.01/1.55 => ( A3
% 3.01/1.55 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_26_equals0D,axiom,
% 3.01/1.55 ! [A: $tType,A3: set @ A,A2: A] :
% 3.01/1.55 ( ( A3
% 3.01/1.55 = ( bot_bot @ ( set @ A ) ) )
% 3.01/1.55 => ~ ( member @ A @ A2 @ A3 ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_27_emptyE,axiom,
% 3.01/1.55 ! [A: $tType,A2: A] :
% 3.01/1.55 ~ ( member @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_28_mk__disjoint__insert,axiom,
% 3.01/1.55 ! [A: $tType,A2: A,A3: set @ A] :
% 3.01/1.55 ( ( member @ A @ A2 @ A3 )
% 3.01/1.55 => ? [B4: set @ A] :
% 3.01/1.55 ( ( A3
% 3.01/1.55 = ( insert @ A @ A2 @ B4 ) )
% 3.01/1.55 & ~ ( member @ A @ A2 @ B4 ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_29_insert__commute,axiom,
% 3.01/1.55 ! [A: $tType,X: A,Y2: A,A3: set @ A] :
% 3.01/1.55 ( ( insert @ A @ X @ ( insert @ A @ Y2 @ A3 ) )
% 3.01/1.55 = ( insert @ A @ Y2 @ ( insert @ A @ X @ A3 ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_30_insert__eq__iff,axiom,
% 3.01/1.55 ! [A: $tType,A2: A,A3: set @ A,B2: A,B: set @ A] :
% 3.01/1.55 ( ~ ( member @ A @ A2 @ A3 )
% 3.01/1.55 => ( ~ ( member @ A @ B2 @ B )
% 3.01/1.55 => ( ( ( insert @ A @ A2 @ A3 )
% 3.01/1.55 = ( insert @ A @ B2 @ B ) )
% 3.01/1.55 = ( ( ( A2 = B2 )
% 3.01/1.55 => ( A3 = B ) )
% 3.01/1.55 & ( ( A2 != B2 )
% 3.01/1.55 => ? [C3: set @ A] :
% 3.01/1.55 ( ( A3
% 3.01/1.55 = ( insert @ A @ B2 @ C3 ) )
% 3.01/1.55 & ~ ( member @ A @ B2 @ C3 )
% 3.01/1.55 & ( B
% 3.01/1.55 = ( insert @ A @ A2 @ C3 ) )
% 3.01/1.55 & ~ ( member @ A @ A2 @ C3 ) ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_31_insert__absorb,axiom,
% 3.01/1.55 ! [A: $tType,A2: A,A3: set @ A] :
% 3.01/1.55 ( ( member @ A @ A2 @ A3 )
% 3.01/1.55 => ( ( insert @ A @ A2 @ A3 )
% 3.01/1.55 = A3 ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_32_insert__ident,axiom,
% 3.01/1.55 ! [A: $tType,X: A,A3: set @ A,B: set @ A] :
% 3.01/1.55 ( ~ ( member @ A @ X @ A3 )
% 3.01/1.55 => ( ~ ( member @ A @ X @ B )
% 3.01/1.55 => ( ( ( insert @ A @ X @ A3 )
% 3.01/1.55 = ( insert @ A @ X @ B ) )
% 3.01/1.55 = ( A3 = B ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_33_Set_Oset__insert,axiom,
% 3.01/1.55 ! [A: $tType,X: A,A3: set @ A] :
% 3.01/1.55 ( ( member @ A @ X @ A3 )
% 3.01/1.55 => ~ ! [B4: set @ A] :
% 3.01/1.55 ( ( A3
% 3.01/1.55 = ( insert @ A @ X @ B4 ) )
% 3.01/1.55 => ( member @ A @ X @ B4 ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_34_insertI2,axiom,
% 3.01/1.55 ! [A: $tType,A2: A,B: set @ A,B2: A] :
% 3.01/1.55 ( ( member @ A @ A2 @ B )
% 3.01/1.55 => ( member @ A @ A2 @ ( insert @ A @ B2 @ B ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_35_insertI1,axiom,
% 3.01/1.55 ! [A: $tType,A2: A,B: set @ A] : ( member @ A @ A2 @ ( insert @ A @ A2 @ B ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_36_insertE,axiom,
% 3.01/1.55 ! [A: $tType,A2: A,B2: A,A3: set @ A] :
% 3.01/1.55 ( ( member @ A @ A2 @ ( insert @ A @ B2 @ A3 ) )
% 3.01/1.55 => ( ( A2 != B2 )
% 3.01/1.55 => ( member @ A @ A2 @ A3 ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_37_singleton__inject,axiom,
% 3.01/1.55 ! [A: $tType,A2: A,B2: A] :
% 3.01/1.55 ( ( ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 3.01/1.55 = ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 3.01/1.55 => ( A2 = B2 ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_38_insert__not__empty,axiom,
% 3.01/1.55 ! [A: $tType,A2: A,A3: set @ A] :
% 3.01/1.55 ( ( insert @ A @ A2 @ A3 )
% 3.01/1.55 != ( bot_bot @ ( set @ A ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_39_doubleton__eq__iff,axiom,
% 3.01/1.55 ! [A: $tType,A2: A,B2: A,C: A,D2: A] :
% 3.01/1.55 ( ( ( insert @ A @ A2 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 3.01/1.55 = ( insert @ A @ C @ ( insert @ A @ D2 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 3.01/1.55 = ( ( ( A2 = C )
% 3.01/1.55 & ( B2 = D2 ) )
% 3.01/1.55 | ( ( A2 = D2 )
% 3.01/1.55 & ( B2 = C ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_40_singleton__iff,axiom,
% 3.01/1.55 ! [A: $tType,B2: A,A2: A] :
% 3.01/1.55 ( ( member @ A @ B2 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 3.01/1.55 = ( B2 = A2 ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_41_the__elem__eq,axiom,
% 3.01/1.55 ! [A: $tType,X: A] :
% 3.01/1.55 ( ( the_elem @ A @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 3.01/1.55 = X ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_42_is__singletonI,axiom,
% 3.01/1.55 ! [A: $tType,X: A] : ( is_singleton @ A @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_43_a11,axiom,
% 3.01/1.55 ine @ p @ ( secrecy_kE @ key ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_44_TBtheorem3b,axiom,
% 3.01/1.55 ! [P: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.01/1.55 ( ~ ( ineM @ P @ M @ E )
% 3.01/1.55 => ( ~ ( ineM @ Q @ M @ E )
% 3.01/1.55 => ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correctCompositionIn @ PQ )
% 3.01/1.55 => ~ ( ineM @ PQ @ M @ E ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_45_mem__Collect__eq,axiom,
% 3.01/1.55 ! [A: $tType,A2: A,P: A > $o] :
% 3.01/1.55 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 3.01/1.55 = ( P @ A2 ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_46_Collect__mem__eq,axiom,
% 3.01/1.55 ! [A: $tType,A3: set @ A] :
% 3.01/1.55 ( ( collect @ A
% 3.01/1.55 @ ^ [X2: A] : ( member @ A @ X2 @ A3 ) )
% 3.01/1.55 = A3 ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_47_Collect__cong,axiom,
% 3.01/1.55 ! [A: $tType,P: A > $o,Q: A > $o] :
% 3.01/1.55 ( ! [X3: A] :
% 3.01/1.55 ( ( P @ X3 )
% 3.01/1.55 = ( Q @ X3 ) )
% 3.01/1.55 => ( ( collect @ A @ P )
% 3.01/1.55 = ( collect @ A @ Q ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_48_ext,axiom,
% 3.01/1.55 ! [B3: $tType,A: $tType,F: A > B3,G: A > B3] :
% 3.01/1.55 ( ! [X3: A] :
% 3.01/1.55 ( ( F @ X3 )
% 3.01/1.55 = ( G @ X3 ) )
% 3.01/1.55 => ( F = G ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_49_TBtheorem1b,axiom,
% 3.01/1.55 ! [PQ: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 3.01/1.55 ( ( ineM @ PQ @ M @ E )
% 3.01/1.55 => ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correctCompositionIn @ PQ )
% 3.01/1.55 => ( ( ineM @ P @ M @ E )
% 3.01/1.55 | ( ineM @ Q @ M @ E ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_50_a11ext,axiom,
% 3.01/1.55 ( ( ine @ p @ ( secrecy_kE @ key ) )
% 3.01/1.55 | ( ine @ q @ ( secrecy_kE @ key ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_51_Set_Ois__empty__def,axiom,
% 3.01/1.55 ! [A: $tType] :
% 3.01/1.55 ( ( is_empty @ A )
% 3.01/1.55 = ( ^ [A4: set @ A] :
% 3.01/1.55 ( A4
% 3.01/1.55 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_52_correctCompositionIn__prop1,axiom,
% 3.01/1.55 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,X: secrecy_chanID] :
% 3.01/1.55 ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correctCompositionIn @ PQ )
% 3.01/1.55 => ( ( member @ secrecy_chanID @ X @ ( ins @ PQ ) )
% 3.01/1.55 => ( ( member @ secrecy_chanID @ X @ ( ins @ P ) )
% 3.01/1.55 | ( member @ secrecy_chanID @ X @ ( ins @ Q ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_53_correctCompositionIn__L2,axiom,
% 3.01/1.55 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID] :
% 3.01/1.55 ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correctCompositionIn @ PQ )
% 3.01/1.55 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 3.01/1.55 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 3.01/1.55 | ( member @ secrecy_chanID @ Ch @ ( ins @ Q ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_54_is__singleton__def,axiom,
% 3.01/1.55 ! [A: $tType] :
% 3.01/1.55 ( ( is_singleton @ A )
% 3.01/1.55 = ( ^ [A4: set @ A] :
% 3.01/1.55 ? [X2: A] :
% 3.01/1.55 ( A4
% 3.01/1.55 = ( insert @ A @ X2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_55_Expression_Oinject_I1_J,axiom,
% 3.01/1.55 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 3.01/1.55 ( ( ( secrecy_kE @ X1 )
% 3.01/1.55 = ( secrecy_kE @ Y1 ) )
% 3.01/1.55 = ( X1 = Y1 ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_56_not__ine__ineM,axiom,
% 3.01/1.55 ! [P: secrecy_specID,E: secrecy_Expression,M: set @ secrecy_chanID] :
% 3.01/1.55 ( ~ ( ine @ P @ E )
% 3.01/1.55 => ~ ( ineM @ P @ M @ E ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_57_ineM__ine,axiom,
% 3.01/1.55 ! [P: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression] :
% 3.01/1.55 ( ( ineM @ P @ M @ E )
% 3.01/1.55 => ( ine @ P @ E ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_58_not__know__k__not__ine,axiom,
% 3.01/1.55 ! [A3: secrecy_specID,M2: secrecy_Keys] :
% 3.01/1.55 ( ~ ( knowle1437066798e_know @ A3 @ ( secrecy_kKS @ M2 ) )
% 3.01/1.55 => ~ ( ine @ A3 @ ( secrecy_kE @ M2 ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_59_is__singleton__the__elem,axiom,
% 3.01/1.55 ! [A: $tType] :
% 3.01/1.55 ( ( is_singleton @ A )
% 3.01/1.55 = ( ^ [A4: set @ A] :
% 3.01/1.55 ( A4
% 3.01/1.55 = ( insert @ A @ ( the_elem @ A @ A4 ) @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_60_is__singletonI_H,axiom,
% 3.01/1.55 ! [A: $tType,A3: set @ A] :
% 3.01/1.55 ( ( A3
% 3.01/1.55 != ( bot_bot @ ( set @ A ) ) )
% 3.01/1.55 => ( ! [X3: A,Y: A] :
% 3.01/1.55 ( ( member @ A @ X3 @ A3 )
% 3.01/1.55 => ( ( member @ A @ Y @ A3 )
% 3.01/1.55 => ( X3 = Y ) ) )
% 3.01/1.55 => ( is_singleton @ A @ A3 ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_61_TBtheorem1a,axiom,
% 3.01/1.55 ! [PQ: secrecy_specID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 3.01/1.55 ( ( ine @ PQ @ E )
% 3.01/1.55 => ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correctCompositionIn @ PQ )
% 3.01/1.55 => ( ( ine @ P @ E )
% 3.01/1.55 | ( ine @ Q @ E ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_62_TBtheorem3a,axiom,
% 3.01/1.55 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.01/1.55 ( ~ ( ine @ P @ E )
% 3.01/1.55 => ( ~ ( ine @ Q @ E )
% 3.01/1.55 => ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correctCompositionIn @ PQ )
% 3.01/1.55 => ~ ( ine @ PQ @ E ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_63_is__singletonE,axiom,
% 3.01/1.55 ! [A: $tType,A3: set @ A] :
% 3.01/1.55 ( ( is_singleton @ A @ A3 )
% 3.01/1.55 => ~ ! [X3: A] :
% 3.01/1.55 ( A3
% 3.01/1.55 != ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_64_bot__empty__eq,axiom,
% 3.01/1.55 ! [A: $tType] :
% 3.01/1.55 ( ( bot_bot @ ( A > $o ) )
% 3.01/1.55 = ( ^ [X2: A] : ( member @ A @ X2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_65_Collect__empty__eq__bot,axiom,
% 3.01/1.55 ! [A: $tType,P: A > $o] :
% 3.01/1.55 ( ( ( collect @ A @ P )
% 3.01/1.55 = ( bot_bot @ ( set @ A ) ) )
% 3.01/1.55 = ( P
% 3.01/1.55 = ( bot_bot @ ( A > $o ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_66_TBlemma3b,axiom,
% 3.01/1.55 ! [P: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID,Ch: secrecy_chanID] :
% 3.01/1.55 ( ~ ( ineM @ P @ M @ E )
% 3.01/1.55 => ( ~ ( ineM @ Q @ M @ E )
% 3.01/1.55 => ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correctCompositionIn @ PQ )
% 3.01/1.55 => ( ( member @ secrecy_chanID @ Ch @ M )
% 3.01/1.55 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 3.01/1.55 => ~ ( exprChannel @ Ch @ E ) ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_67_correctCompositionIn__L1,axiom,
% 3.01/1.55 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID] :
% 3.01/1.55 ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correctCompositionIn @ PQ )
% 3.01/1.55 => ( ~ ( member @ secrecy_chanID @ Ch @ ( loc @ PQ ) )
% 3.01/1.55 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 3.01/1.55 => ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_68_KS2Expression_Osimps_I1_J,axiom,
% 3.01/1.55 ! [M2: secrecy_Keys] :
% 3.01/1.55 ( ( secrec1016742679ession @ ( secrecy_kKS @ M2 ) )
% 3.01/1.55 = ( secrecy_kE @ M2 ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_69_TBtheorem4a__empty,axiom,
% 3.01/1.55 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.01/1.55 ( ( ( ine @ P @ E )
% 3.01/1.55 | ( ine @ Q @ E ) )
% 3.01/1.55 => ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correctCompositionIn @ PQ )
% 3.01/1.55 => ( ( ( loc @ PQ )
% 3.01/1.55 = ( bot_bot @ ( set @ secrecy_chanID ) ) )
% 3.01/1.55 => ( ine @ PQ @ E ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_70_know_Osimps_I1_J,axiom,
% 3.01/1.55 ! [A3: secrecy_specID,M2: secrecy_Keys] :
% 3.01/1.55 ( ( knowle1437066798e_know @ A3 @ ( secrecy_kKS @ M2 ) )
% 3.01/1.55 = ( ( ine @ A3 @ ( secrecy_kE @ M2 ) )
% 3.01/1.55 | ( member @ secrecy_KS @ ( secrecy_kKS @ M2 ) @ ( localSecrets @ A3 ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_71_correctCompositionKS__exprChannel__k__P,axiom,
% 3.01/1.55 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 3.01/1.55 ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correctCompositionKS @ PQ )
% 3.01/1.55 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 3.01/1.55 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 3.01/1.55 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 3.01/1.55 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 3.01/1.55 => ( ( correctCompositionIn @ PQ )
% 3.01/1.55 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 3.01/1.55 & ( exprChannel @ Ch @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_72_LocalSecretsComposition__neg__loc__k,axiom,
% 3.01/1.55 ! [Key: secrecy_Keys,P: secrecy_specID,Ch: secrecy_chanID] :
% 3.01/1.55 ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ P ) )
% 3.01/1.55 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 3.01/1.55 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ P ) )
% 3.01/1.55 => ~ ( member @ secrecy_chanID @ Ch @ ( loc @ P ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_73_LocalSecretsComposition1,axiom,
% 3.01/1.55 ! [Ls: secrecy_KS,P: secrecy_specID,PQ: secrecy_specID,Q: secrecy_specID] :
% 3.01/1.55 ( ( member @ secrecy_KS @ Ls @ ( localSecrets @ P ) )
% 3.01/1.55 => ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( member @ secrecy_KS @ Ls @ ( localSecrets @ PQ ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_74_LocalSecretsComposition__exprChannel__k,axiom,
% 3.01/1.55 ! [X: secrecy_chanID,Keys: secrecy_Keys,P: secrecy_specID,Q: secrecy_specID] :
% 3.01/1.55 ( ( exprChannel @ X @ ( secrecy_kE @ Keys ) )
% 3.01/1.55 => ( ~ ( ine @ P @ ( secrecy_kE @ Keys ) )
% 3.01/1.55 => ( ~ ( ine @ Q @ ( secrecy_kE @ Keys ) )
% 3.01/1.55 => ( ~ ( member @ secrecy_chanID @ X @ ( ins @ P ) )
% 3.01/1.55 & ~ ( member @ secrecy_chanID @ X @ ( ins @ Q ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_75_ine__def,axiom,
% 3.01/1.55 ( ine
% 3.01/1.55 = ( ^ [SP: secrecy_specID,E2: secrecy_Expression] :
% 3.01/1.55 ? [Ch2: secrecy_chanID] :
% 3.01/1.55 ( ( member @ secrecy_chanID @ Ch2 @ ( ins @ SP ) )
% 3.01/1.55 & ( exprChannel @ Ch2 @ E2 ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_76_ine__ins__neg1,axiom,
% 3.01/1.55 ! [P: secrecy_specID,M2: secrecy_Expression,X: secrecy_chanID] :
% 3.01/1.55 ( ~ ( ine @ P @ M2 )
% 3.01/1.55 => ( ( exprChannel @ X @ M2 )
% 3.01/1.55 => ~ ( member @ secrecy_chanID @ X @ ( ins @ P ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_77_ineM__L1,axiom,
% 3.01/1.55 ! [Ch: secrecy_chanID,M: set @ secrecy_chanID,P: secrecy_specID,E: secrecy_Expression] :
% 3.01/1.55 ( ( member @ secrecy_chanID @ Ch @ M )
% 3.01/1.55 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 3.01/1.55 => ( ( exprChannel @ Ch @ E )
% 3.01/1.55 => ( ineM @ P @ M @ E ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_78_ineM__def,axiom,
% 3.01/1.55 ( ineM
% 3.01/1.55 = ( ^ [SP: secrecy_specID,M3: set @ secrecy_chanID,E2: secrecy_Expression] :
% 3.01/1.55 ? [Ch2: secrecy_chanID] :
% 3.01/1.55 ( ( member @ secrecy_chanID @ Ch2 @ ( ins @ SP ) )
% 3.01/1.55 & ( member @ secrecy_chanID @ Ch2 @ M3 )
% 3.01/1.55 & ( exprChannel @ Ch2 @ E2 ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_79_correctCompositionInLoc__exprChannel,axiom,
% 3.01/1.55 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID,M2: secrecy_Expression] :
% 3.01/1.55 ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correctCompositionIn @ PQ )
% 3.01/1.55 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 3.01/1.55 => ( ( exprChannel @ Ch @ M2 )
% 3.01/1.55 => ( ! [X3: secrecy_chanID] :
% 3.01/1.55 ( ( member @ secrecy_chanID @ X3 @ ( ins @ PQ ) )
% 3.01/1.55 => ~ ( exprChannel @ X3 @ M2 ) )
% 3.01/1.55 => ( member @ secrecy_chanID @ Ch @ ( loc @ PQ ) ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_80_TBtheorem4a__PQ,axiom,
% 3.01/1.55 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.01/1.55 ( ( ( ine @ P @ E )
% 3.01/1.55 | ( ine @ Q @ E ) )
% 3.01/1.55 => ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correctCompositionIn @ PQ )
% 3.01/1.55 => ( ? [Ch3: secrecy_chanID] :
% 3.01/1.55 ( ( ( member @ secrecy_chanID @ Ch3 @ ( ins @ P ) )
% 3.01/1.55 | ( member @ secrecy_chanID @ Ch3 @ ( ins @ Q ) ) )
% 3.01/1.55 & ( exprChannel @ Ch3 @ E )
% 3.01/1.55 & ~ ( member @ secrecy_chanID @ Ch3 @ ( loc @ PQ ) ) )
% 3.01/1.55 => ( ine @ PQ @ E ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_81_TBtheorem4a__P,axiom,
% 3.01/1.55 ! [P: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 3.01/1.55 ( ( ine @ P @ E )
% 3.01/1.55 => ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correctCompositionIn @ PQ )
% 3.01/1.55 => ( ? [Ch3: secrecy_chanID] :
% 3.01/1.55 ( ( member @ secrecy_chanID @ Ch3 @ ( ins @ P ) )
% 3.01/1.55 & ( exprChannel @ Ch3 @ E )
% 3.01/1.55 & ~ ( member @ secrecy_chanID @ Ch3 @ ( loc @ PQ ) ) )
% 3.01/1.55 => ( ine @ PQ @ E ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_82_TBtheorem4b__PQ,axiom,
% 3.01/1.55 ! [P: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.01/1.55 ( ( ( ineM @ P @ M @ E )
% 3.01/1.55 | ( ineM @ Q @ M @ E ) )
% 3.01/1.55 => ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correctCompositionIn @ PQ )
% 3.01/1.55 => ( ? [Ch3: secrecy_chanID] :
% 3.01/1.55 ( ( ( member @ secrecy_chanID @ Ch3 @ ( ins @ P ) )
% 3.01/1.55 | ( member @ secrecy_chanID @ Ch3 @ ( ins @ Q ) ) )
% 3.01/1.55 & ( member @ secrecy_chanID @ Ch3 @ M )
% 3.01/1.55 & ( exprChannel @ Ch3 @ E )
% 3.01/1.55 & ~ ( member @ secrecy_chanID @ Ch3 @ ( loc @ PQ ) ) )
% 3.01/1.55 => ( ineM @ PQ @ M @ E ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_83_TBtheorem4b__P,axiom,
% 3.01/1.55 ! [P: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 3.01/1.55 ( ( ineM @ P @ M @ E )
% 3.01/1.55 => ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correctCompositionIn @ PQ )
% 3.01/1.55 => ( ? [Ch3: secrecy_chanID] :
% 3.01/1.55 ( ( member @ secrecy_chanID @ Ch3 @ ( ins @ Q ) )
% 3.01/1.55 & ( exprChannel @ Ch3 @ E )
% 3.01/1.55 & ~ ( member @ secrecy_chanID @ Ch3 @ ( loc @ PQ ) )
% 3.01/1.55 & ( member @ secrecy_chanID @ Ch3 @ M ) )
% 3.01/1.55 => ( ineM @ PQ @ M @ E ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_84_correctCompositionKS__exprChannel__k__Qex,axiom,
% 3.01/1.55 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 3.01/1.55 ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correctCompositionKS @ PQ )
% 3.01/1.55 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 3.01/1.55 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ Q ) )
% 3.01/1.55 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 3.01/1.55 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 3.01/1.55 => ( ( correctCompositionIn @ PQ )
% 3.01/1.55 => ? [Ch4: secrecy_chanID] :
% 3.01/1.55 ( ( member @ secrecy_chanID @ Ch4 @ ( ins @ PQ ) )
% 3.01/1.55 & ( exprChannel @ Ch4 @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_85_correctCompositionKS__exprChannel__k__Pex,axiom,
% 3.01/1.55 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 3.01/1.55 ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correctCompositionKS @ PQ )
% 3.01/1.55 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 3.01/1.55 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 3.01/1.55 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 3.01/1.55 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 3.01/1.55 => ( ( correctCompositionIn @ PQ )
% 3.01/1.55 => ? [Ch4: secrecy_chanID] :
% 3.01/1.55 ( ( member @ secrecy_chanID @ Ch4 @ ( ins @ PQ ) )
% 3.01/1.55 & ( exprChannel @ Ch4 @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_86_correctCompositionKS__exprChannel__k__Q,axiom,
% 3.01/1.55 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 3.01/1.55 ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correctCompositionKS @ PQ )
% 3.01/1.55 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 3.01/1.55 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ Q ) )
% 3.01/1.55 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 3.01/1.55 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 3.01/1.55 => ( ( correctCompositionIn @ PQ )
% 3.01/1.55 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 3.01/1.55 & ( exprChannel @ Ch @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_87_TBtheorem4b__notP1,axiom,
% 3.01/1.55 ! [P: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.01/1.55 ( ( ineM @ P @ M @ E )
% 3.01/1.55 => ( ~ ( ineM @ Q @ M @ E )
% 3.01/1.55 => ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correctCompositionIn @ PQ )
% 3.01/1.55 => ( ? [Ch3: secrecy_chanID] :
% 3.01/1.55 ( ( ine_ex1303305700Single @ P @ Ch3 @ E )
% 3.01/1.55 & ( member @ secrecy_chanID @ Ch3 @ M )
% 3.01/1.55 & ( member @ secrecy_chanID @ Ch3 @ ( loc @ PQ ) ) )
% 3.01/1.55 => ~ ( ineM @ PQ @ M @ E ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_88_TBtheorem4a__notP1,axiom,
% 3.01/1.55 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.01/1.55 ( ( ine @ P @ E )
% 3.01/1.55 => ( ~ ( ine @ Q @ E )
% 3.01/1.55 => ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correctCompositionIn @ PQ )
% 3.01/1.55 => ( ? [Ch3: secrecy_chanID] :
% 3.01/1.55 ( ( ine_ex1303305700Single @ P @ Ch3 @ E )
% 3.01/1.55 & ( member @ secrecy_chanID @ Ch3 @ ( loc @ PQ ) ) )
% 3.01/1.55 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_89_LocalSecretsComposition__neg1__k,axiom,
% 3.01/1.55 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Keys: secrecy_Keys] :
% 3.01/1.55 ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correc965049635ionLoc @ PQ )
% 3.01/1.55 => ( ~ ( ine @ P @ ( secrecy_kE @ Keys ) )
% 3.01/1.55 => ( ~ ( ine @ Q @ ( secrecy_kE @ Keys ) )
% 3.01/1.55 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ P ) )
% 3.01/1.55 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ Q ) )
% 3.01/1.55 => ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_90_LocalSecretsComposition__ine2__k,axiom,
% 3.01/1.55 ! [K: secrecy_Keys,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 3.01/1.55 ( ( member @ secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ PQ ) )
% 3.01/1.55 => ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correc965049635ionLoc @ PQ )
% 3.01/1.55 => ( ~ ( ine @ P @ ( secrecy_kE @ K ) )
% 3.01/1.55 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ P ) )
% 3.01/1.55 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ Q ) )
% 3.01/1.55 => ( ine @ Q @ ( secrecy_kE @ K ) ) ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_91_LocalSecretsComposition__ine1__k,axiom,
% 3.01/1.55 ! [K: secrecy_Keys,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 3.01/1.55 ( ( member @ secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ PQ ) )
% 3.01/1.55 => ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correc965049635ionLoc @ PQ )
% 3.01/1.55 => ( ~ ( ine @ Q @ ( secrecy_kE @ K ) )
% 3.01/1.55 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ P ) )
% 3.01/1.55 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ Q ) )
% 3.01/1.55 => ( ine @ P @ ( secrecy_kE @ K ) ) ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_92_TBtheorem4b__notPQ,axiom,
% 3.01/1.55 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set @ secrecy_chanID,E: secrecy_Expression,ChSetQ: set @ secrecy_chanID,M: set @ secrecy_chanID] :
% 3.01/1.55 ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correctCompositionIn @ PQ )
% 3.01/1.55 => ( ( ine_exprChannelSet @ P @ ChSetP @ E )
% 3.01/1.55 => ( ( ine_exprChannelSet @ Q @ ChSetQ @ E )
% 3.01/1.55 => ( ! [X3: secrecy_chanID] :
% 3.01/1.55 ( ( member @ secrecy_chanID @ X3 @ ChSetP )
% 3.01/1.55 => ( member @ secrecy_chanID @ X3 @ ( loc @ PQ ) ) )
% 3.01/1.55 => ( ! [X3: secrecy_chanID] :
% 3.01/1.55 ( ( member @ secrecy_chanID @ X3 @ ChSetQ )
% 3.01/1.55 => ( member @ secrecy_chanID @ X3 @ ( loc @ PQ ) ) )
% 3.01/1.55 => ~ ( ineM @ PQ @ M @ E ) ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_93_TBtheorem4b__notP2,axiom,
% 3.01/1.55 ! [Q: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set @ secrecy_chanID] :
% 3.01/1.55 ( ~ ( ineM @ Q @ M @ E )
% 3.01/1.55 => ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correctCompositionIn @ PQ )
% 3.01/1.55 => ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 3.01/1.55 => ( ! [X3: secrecy_chanID] :
% 3.01/1.55 ( ( member @ secrecy_chanID @ X3 @ ChSet )
% 3.01/1.55 => ( member @ secrecy_chanID @ X3 @ ( loc @ PQ ) ) )
% 3.01/1.55 => ~ ( ineM @ PQ @ M @ E ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_94_ine__exprChannelSingle__Set,axiom,
% 3.01/1.55 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 3.01/1.55 ( ( ine_ex1303305700Single @ P @ Ch @ E )
% 3.01/1.55 => ( ine_exprChannelSet @ P @ ( insert @ secrecy_chanID @ Ch @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ E ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_95_ine__exprChannelSet__Single,axiom,
% 3.01/1.55 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 3.01/1.55 ( ( ine_exprChannelSet @ P @ ( insert @ secrecy_chanID @ Ch @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ E )
% 3.01/1.55 => ( ine_ex1303305700Single @ P @ Ch @ E ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_96_ine__exprChannelSet__def,axiom,
% 3.01/1.55 ( ine_exprChannelSet
% 3.01/1.55 = ( ^ [SP: secrecy_specID,ChSet2: set @ secrecy_chanID,E2: secrecy_Expression] :
% 3.01/1.55 ( ! [X2: secrecy_chanID] :
% 3.01/1.55 ( ( member @ secrecy_chanID @ X2 @ ChSet2 )
% 3.01/1.55 => ( ( member @ secrecy_chanID @ X2 @ ( ins @ SP ) )
% 3.01/1.55 & ( exprChannel @ X2 @ E2 ) ) )
% 3.01/1.55 & ! [X2: secrecy_chanID] :
% 3.01/1.55 ( ( ~ ( member @ secrecy_chanID @ X2 @ ChSet2 )
% 3.01/1.55 & ( member @ secrecy_chanID @ X2 @ ( ins @ SP ) ) )
% 3.01/1.55 => ~ ( exprChannel @ X2 @ E2 ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_97_ine__empty__exprChannelSet,axiom,
% 3.01/1.55 ! [P: secrecy_specID,ChSet: set @ secrecy_chanID,E: secrecy_Expression] :
% 3.01/1.55 ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 3.01/1.55 => ( ( ChSet
% 3.01/1.55 = ( bot_bot @ ( set @ secrecy_chanID ) ) )
% 3.01/1.55 => ~ ( ine @ P @ E ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_98_ine__nonempty__exprChannelSet,axiom,
% 3.01/1.55 ! [P: secrecy_specID,ChSet: set @ secrecy_chanID,E: secrecy_Expression] :
% 3.01/1.55 ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 3.01/1.55 => ( ( ChSet
% 3.01/1.55 != ( bot_bot @ ( set @ secrecy_chanID ) ) )
% 3.01/1.55 => ( ine @ P @ E ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_99_ine__exprChannelSingle__def,axiom,
% 3.01/1.55 ( ine_ex1303305700Single
% 3.01/1.55 = ( ^ [SP: secrecy_specID,Ch2: secrecy_chanID,E2: secrecy_Expression] :
% 3.01/1.55 ( ( member @ secrecy_chanID @ Ch2 @ ( ins @ SP ) )
% 3.01/1.55 & ( exprChannel @ Ch2 @ E2 )
% 3.01/1.55 & ! [X2: secrecy_chanID,T: nat] :
% 3.01/1.55 ( ( ( member @ secrecy_chanID @ X2 @ ( ins @ SP ) )
% 3.01/1.55 & ( X2 != Ch2 ) )
% 3.01/1.55 => ~ ( exprChannel @ X2 @ E2 ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_100_TBtheorem4a__notP2,axiom,
% 3.01/1.55 ! [Q: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set @ secrecy_chanID] :
% 3.01/1.55 ( ~ ( ine @ Q @ E )
% 3.01/1.55 => ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correctCompositionIn @ PQ )
% 3.01/1.55 => ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 3.01/1.55 => ( ! [X3: secrecy_chanID] :
% 3.01/1.55 ( ( member @ secrecy_chanID @ X3 @ ChSet )
% 3.01/1.55 => ( member @ secrecy_chanID @ X3 @ ( loc @ PQ ) ) )
% 3.01/1.55 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_101_TBtheorem4a__notPQ,axiom,
% 3.01/1.55 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set @ secrecy_chanID,E: secrecy_Expression,ChSetQ: set @ secrecy_chanID] :
% 3.01/1.55 ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correctCompositionIn @ PQ )
% 3.01/1.55 => ( ( ine_exprChannelSet @ P @ ChSetP @ E )
% 3.01/1.55 => ( ( ine_exprChannelSet @ Q @ ChSetQ @ E )
% 3.01/1.55 => ( ! [X3: secrecy_chanID] :
% 3.01/1.55 ( ( member @ secrecy_chanID @ X3 @ ChSetP )
% 3.01/1.55 => ( member @ secrecy_chanID @ X3 @ ( loc @ PQ ) ) )
% 3.01/1.55 => ( ! [X3: secrecy_chanID] :
% 3.01/1.55 ( ( member @ secrecy_chanID @ X3 @ ChSetQ )
% 3.01/1.55 => ( member @ secrecy_chanID @ X3 @ ( loc @ PQ ) ) )
% 3.01/1.55 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_102_subcomponents__loc,axiom,
% 3.01/1.55 ! [X: secrecy_specID] :
% 3.01/1.55 ( ( correc965049635ionLoc @ X )
% 3.01/1.55 => ( ( ( subcomponents @ X )
% 3.01/1.55 = ( bot_bot @ ( set @ secrecy_specID ) ) )
% 3.01/1.55 => ( ( loc @ X )
% 3.01/1.55 = ( bot_bot @ ( set @ secrecy_chanID ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_103_LocalSecretsComposition__neg__k,axiom,
% 3.01/1.55 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,M2: secrecy_Keys] :
% 3.01/1.55 ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correc965049635ionLoc @ PQ )
% 3.01/1.55 => ( ( correctCompositionKS @ PQ )
% 3.01/1.55 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ M2 ) @ ( specKeysSecrets @ P ) )
% 3.01/1.55 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ M2 ) @ ( specKeysSecrets @ Q ) )
% 3.01/1.55 => ( ~ ( ine @ P @ ( secrecy_kE @ M2 ) )
% 3.01/1.55 => ( ~ ( ine @ Q @ ( secrecy_kE @ M2 ) )
% 3.01/1.55 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ M2 ) @ ( sup_sup @ ( set @ secrecy_KS ) @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 3.01/1.55 => ~ ( member @ secrecy_KS @ ( secrecy_kKS @ M2 ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_104_correctCompositionKS__exprChannel__s__P,axiom,
% 3.01/1.55 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 3.01/1.55 ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correctCompositionKS @ PQ )
% 3.01/1.55 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 3.01/1.55 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 3.01/1.55 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 3.01/1.55 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 3.01/1.55 => ( ( correctCompositionIn @ PQ )
% 3.01/1.55 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 3.01/1.55 & ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_105_correctCompositionKS__exprChannel__s__Q,axiom,
% 3.01/1.55 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 3.01/1.55 ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correctCompositionKS @ PQ )
% 3.01/1.55 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 3.01/1.55 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ Q ) )
% 3.01/1.55 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 3.01/1.55 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 3.01/1.55 => ( ( correctCompositionIn @ PQ )
% 3.01/1.55 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 3.01/1.55 & ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_106_correctCompositionKS__exprChannel__s__Pex,axiom,
% 3.01/1.55 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 3.01/1.55 ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correctCompositionKS @ PQ )
% 3.01/1.55 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 3.01/1.55 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 3.01/1.55 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 3.01/1.55 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 3.01/1.55 => ( ( correctCompositionIn @ PQ )
% 3.01/1.55 => ? [Ch4: secrecy_chanID] :
% 3.01/1.55 ( ( member @ secrecy_chanID @ Ch4 @ ( ins @ PQ ) )
% 3.01/1.55 & ( exprChannel @ Ch4 @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_107_UnCI,axiom,
% 3.01/1.55 ! [A: $tType,C: A,B: set @ A,A3: set @ A] :
% 3.01/1.55 ( ( ~ ( member @ A @ C @ B )
% 3.01/1.55 => ( member @ A @ C @ A3 ) )
% 3.01/1.55 => ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A3 @ B ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_108_Un__iff,axiom,
% 3.01/1.55 ! [A: $tType,C: A,A3: set @ A,B: set @ A] :
% 3.01/1.55 ( ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A3 @ B ) )
% 3.01/1.55 = ( ( member @ A @ C @ A3 )
% 3.01/1.55 | ( member @ A @ C @ B ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_109_KS_Oinject_I2_J,axiom,
% 3.01/1.55 ! [X22: secrecy_Secrets,Y22: secrecy_Secrets] :
% 3.01/1.55 ( ( ( secrecy_sKS @ X22 )
% 3.01/1.55 = ( secrecy_sKS @ Y22 ) )
% 3.01/1.55 = ( X22 = Y22 ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_110_Expression_Oinject_I2_J,axiom,
% 3.01/1.55 ! [X22: secrecy_Secrets,Y22: secrecy_Secrets] :
% 3.01/1.55 ( ( ( secrecy_sE @ X22 )
% 3.01/1.55 = ( secrecy_sE @ Y22 ) )
% 3.01/1.55 = ( X22 = Y22 ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_111_Un__empty,axiom,
% 3.01/1.55 ! [A: $tType,A3: set @ A,B: set @ A] :
% 3.01/1.55 ( ( ( sup_sup @ ( set @ A ) @ A3 @ B )
% 3.01/1.55 = ( bot_bot @ ( set @ A ) ) )
% 3.01/1.55 = ( ( A3
% 3.01/1.55 = ( bot_bot @ ( set @ A ) ) )
% 3.01/1.55 & ( B
% 3.01/1.55 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_112_Un__insert__right,axiom,
% 3.01/1.55 ! [A: $tType,A3: set @ A,A2: A,B: set @ A] :
% 3.01/1.55 ( ( sup_sup @ ( set @ A ) @ A3 @ ( insert @ A @ A2 @ B ) )
% 3.01/1.55 = ( insert @ A @ A2 @ ( sup_sup @ ( set @ A ) @ A3 @ B ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_113_Un__insert__left,axiom,
% 3.01/1.55 ! [A: $tType,A2: A,B: set @ A,C4: set @ A] :
% 3.01/1.55 ( ( sup_sup @ ( set @ A ) @ ( insert @ A @ A2 @ B ) @ C4 )
% 3.01/1.55 = ( insert @ A @ A2 @ ( sup_sup @ ( set @ A ) @ B @ C4 ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_114_UnE,axiom,
% 3.01/1.55 ! [A: $tType,C: A,A3: set @ A,B: set @ A] :
% 3.01/1.55 ( ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A3 @ B ) )
% 3.01/1.55 => ( ~ ( member @ A @ C @ A3 )
% 3.01/1.55 => ( member @ A @ C @ B ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_115_UnI1,axiom,
% 3.01/1.55 ! [A: $tType,C: A,A3: set @ A,B: set @ A] :
% 3.01/1.55 ( ( member @ A @ C @ A3 )
% 3.01/1.55 => ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A3 @ B ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_116_UnI2,axiom,
% 3.01/1.55 ! [A: $tType,C: A,B: set @ A,A3: set @ A] :
% 3.01/1.55 ( ( member @ A @ C @ B )
% 3.01/1.55 => ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A3 @ B ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_117_bex__Un,axiom,
% 3.01/1.55 ! [A: $tType,A3: set @ A,B: set @ A,P: A > $o] :
% 3.01/1.55 ( ( ? [X2: A] :
% 3.01/1.55 ( ( member @ A @ X2 @ ( sup_sup @ ( set @ A ) @ A3 @ B ) )
% 3.01/1.55 & ( P @ X2 ) ) )
% 3.01/1.55 = ( ? [X2: A] :
% 3.01/1.55 ( ( member @ A @ X2 @ A3 )
% 3.01/1.55 & ( P @ X2 ) )
% 3.01/1.55 | ? [X2: A] :
% 3.01/1.55 ( ( member @ A @ X2 @ B )
% 3.01/1.55 & ( P @ X2 ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_118_ball__Un,axiom,
% 3.01/1.55 ! [A: $tType,A3: set @ A,B: set @ A,P: A > $o] :
% 3.01/1.55 ( ( ! [X2: A] :
% 3.01/1.55 ( ( member @ A @ X2 @ ( sup_sup @ ( set @ A ) @ A3 @ B ) )
% 3.01/1.55 => ( P @ X2 ) ) )
% 3.01/1.55 = ( ! [X2: A] :
% 3.01/1.55 ( ( member @ A @ X2 @ A3 )
% 3.01/1.55 => ( P @ X2 ) )
% 3.01/1.55 & ! [X2: A] :
% 3.01/1.55 ( ( member @ A @ X2 @ B )
% 3.01/1.55 => ( P @ X2 ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_119_Un__assoc,axiom,
% 3.01/1.55 ! [A: $tType,A3: set @ A,B: set @ A,C4: set @ A] :
% 3.01/1.55 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A3 @ B ) @ C4 )
% 3.01/1.55 = ( sup_sup @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ B @ C4 ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_120_Un__absorb,axiom,
% 3.01/1.55 ! [A: $tType,A3: set @ A] :
% 3.01/1.55 ( ( sup_sup @ ( set @ A ) @ A3 @ A3 )
% 3.01/1.55 = A3 ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_121_Un__commute,axiom,
% 3.01/1.55 ! [A: $tType] :
% 3.01/1.55 ( ( sup_sup @ ( set @ A ) )
% 3.01/1.55 = ( ^ [A4: set @ A,B5: set @ A] : ( sup_sup @ ( set @ A ) @ B5 @ A4 ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_122_Un__left__absorb,axiom,
% 3.01/1.55 ! [A: $tType,A3: set @ A,B: set @ A] :
% 3.01/1.55 ( ( sup_sup @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ A3 @ B ) )
% 3.01/1.55 = ( sup_sup @ ( set @ A ) @ A3 @ B ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_123_Un__left__commute,axiom,
% 3.01/1.55 ! [A: $tType,A3: set @ A,B: set @ A,C4: set @ A] :
% 3.01/1.55 ( ( sup_sup @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ B @ C4 ) )
% 3.01/1.55 = ( sup_sup @ ( set @ A ) @ B @ ( sup_sup @ ( set @ A ) @ A3 @ C4 ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_124_KS2Expression_Osimps_I2_J,axiom,
% 3.01/1.55 ! [M2: secrecy_Secrets] :
% 3.01/1.55 ( ( secrec1016742679ession @ ( secrecy_sKS @ M2 ) )
% 3.01/1.55 = ( secrecy_sE @ M2 ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_125_Un__empty__right,axiom,
% 3.01/1.55 ! [A: $tType,A3: set @ A] :
% 3.01/1.55 ( ( sup_sup @ ( set @ A ) @ A3 @ ( bot_bot @ ( set @ A ) ) )
% 3.01/1.55 = A3 ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_126_Un__empty__left,axiom,
% 3.01/1.55 ! [A: $tType,B: set @ A] :
% 3.01/1.55 ( ( sup_sup @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ B )
% 3.01/1.55 = B ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_127_not__know__s__not__ine,axiom,
% 3.01/1.55 ! [A3: secrecy_specID,M2: secrecy_Secrets] :
% 3.01/1.55 ( ~ ( knowle1437066798e_know @ A3 @ ( secrecy_sKS @ M2 ) )
% 3.01/1.55 => ~ ( ine @ A3 @ ( secrecy_sE @ M2 ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_128_KS_Oexhaust,axiom,
% 3.01/1.55 ! [Y2: secrecy_KS] :
% 3.01/1.55 ( ! [X12: secrecy_Keys] :
% 3.01/1.55 ( Y2
% 3.01/1.55 != ( secrecy_kKS @ X12 ) )
% 3.01/1.55 => ~ ! [X23: secrecy_Secrets] :
% 3.01/1.55 ( Y2
% 3.01/1.55 != ( secrecy_sKS @ X23 ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_129_KS_Oinduct,axiom,
% 3.01/1.55 ! [P: secrecy_KS > $o,KS: secrecy_KS] :
% 3.01/1.55 ( ! [X3: secrecy_Keys] : ( P @ ( secrecy_kKS @ X3 ) )
% 3.01/1.55 => ( ! [X3: secrecy_Secrets] : ( P @ ( secrecy_sKS @ X3 ) )
% 3.01/1.55 => ( P @ KS ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_130_KS_Odistinct_I1_J,axiom,
% 3.01/1.55 ! [X1: secrecy_Keys,X22: secrecy_Secrets] :
% 3.01/1.55 ( ( secrecy_kKS @ X1 )
% 3.01/1.55 != ( secrecy_sKS @ X22 ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_131_Expression_Odistinct_I1_J,axiom,
% 3.01/1.55 ! [X1: secrecy_Keys,X22: secrecy_Secrets] :
% 3.01/1.55 ( ( secrecy_kE @ X1 )
% 3.01/1.55 != ( secrecy_sE @ X22 ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_132_know_Osimps_I2_J,axiom,
% 3.01/1.55 ! [A3: secrecy_specID,M2: secrecy_Secrets] :
% 3.01/1.55 ( ( knowle1437066798e_know @ A3 @ ( secrecy_sKS @ M2 ) )
% 3.01/1.55 = ( ( ine @ A3 @ ( secrecy_sE @ M2 ) )
% 3.01/1.55 | ( member @ secrecy_KS @ ( secrecy_sKS @ M2 ) @ ( localSecrets @ A3 ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_133_singleton__Un__iff,axiom,
% 3.01/1.55 ! [A: $tType,X: A,A3: set @ A,B: set @ A] :
% 3.01/1.55 ( ( ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) )
% 3.01/1.55 = ( sup_sup @ ( set @ A ) @ A3 @ B ) )
% 3.01/1.55 = ( ( ( A3
% 3.01/1.55 = ( bot_bot @ ( set @ A ) ) )
% 3.01/1.55 & ( B
% 3.01/1.55 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) )
% 3.01/1.55 | ( ( A3
% 3.01/1.55 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 3.01/1.55 & ( B
% 3.01/1.55 = ( bot_bot @ ( set @ A ) ) ) )
% 3.01/1.55 | ( ( A3
% 3.01/1.55 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 3.01/1.55 & ( B
% 3.01/1.55 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_134_Un__singleton__iff,axiom,
% 3.01/1.55 ! [A: $tType,A3: set @ A,B: set @ A,X: A] :
% 3.01/1.55 ( ( ( sup_sup @ ( set @ A ) @ A3 @ B )
% 3.01/1.55 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 3.01/1.55 = ( ( ( A3
% 3.01/1.55 = ( bot_bot @ ( set @ A ) ) )
% 3.01/1.55 & ( B
% 3.01/1.55 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) )
% 3.01/1.55 | ( ( A3
% 3.01/1.55 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 3.01/1.55 & ( B
% 3.01/1.55 = ( bot_bot @ ( set @ A ) ) ) )
% 3.01/1.55 | ( ( A3
% 3.01/1.55 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 3.01/1.55 & ( B
% 3.01/1.55 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_135_insert__is__Un,axiom,
% 3.01/1.55 ! [A: $tType] :
% 3.01/1.55 ( ( insert @ A )
% 3.01/1.55 = ( ^ [A5: A] : ( sup_sup @ ( set @ A ) @ ( insert @ A @ A5 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_136_LocalSecretsComposition__neg__loc__s,axiom,
% 3.01/1.55 ! [Secret: secrecy_Secrets,P: secrecy_specID,Ch: secrecy_chanID] :
% 3.01/1.55 ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ P ) )
% 3.01/1.55 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 3.01/1.55 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ P ) )
% 3.01/1.55 => ~ ( member @ secrecy_chanID @ Ch @ ( loc @ P ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_137_LocalSecretsComposition__neg__s,axiom,
% 3.01/1.55 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,M2: secrecy_Secrets] :
% 3.01/1.55 ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correc965049635ionLoc @ PQ )
% 3.01/1.55 => ( ( correctCompositionKS @ PQ )
% 3.01/1.55 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ M2 ) @ ( specKeysSecrets @ P ) )
% 3.01/1.55 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ M2 ) @ ( specKeysSecrets @ Q ) )
% 3.01/1.55 => ( ~ ( ine @ P @ ( secrecy_sE @ M2 ) )
% 3.01/1.55 => ( ~ ( ine @ Q @ ( secrecy_sE @ M2 ) )
% 3.01/1.55 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ M2 ) @ ( sup_sup @ ( set @ secrecy_KS ) @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 3.01/1.55 => ~ ( member @ secrecy_KS @ ( secrecy_sKS @ M2 ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_138_LocalSecretsComposition__ine1__s,axiom,
% 3.01/1.55 ! [S: secrecy_Secrets,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 3.01/1.55 ( ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) )
% 3.01/1.55 => ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correc965049635ionLoc @ PQ )
% 3.01/1.55 => ( ~ ( ine @ Q @ ( secrecy_sE @ S ) )
% 3.01/1.55 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 3.01/1.55 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 3.01/1.55 => ( ine @ P @ ( secrecy_sE @ S ) ) ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_139_LocalSecretsComposition__ine2__s,axiom,
% 3.01/1.55 ! [S: secrecy_Secrets,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 3.01/1.55 ( ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) )
% 3.01/1.55 => ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correc965049635ionLoc @ PQ )
% 3.01/1.55 => ( ~ ( ine @ P @ ( secrecy_sE @ S ) )
% 3.01/1.55 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 3.01/1.55 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 3.01/1.55 => ( ine @ Q @ ( secrecy_sE @ S ) ) ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_140_LocalSecretsComposition__neg1__s,axiom,
% 3.01/1.55 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,S: secrecy_Secrets] :
% 3.01/1.55 ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correc965049635ionLoc @ PQ )
% 3.01/1.55 => ( ~ ( ine @ P @ ( secrecy_sE @ S ) )
% 3.01/1.55 => ( ~ ( ine @ Q @ ( secrecy_sE @ S ) )
% 3.01/1.55 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 3.01/1.55 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 3.01/1.55 => ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_141_LocalSecretsComposition__exprChannel__s,axiom,
% 3.01/1.55 ! [X: secrecy_chanID,Secrets: secrecy_Secrets,P: secrecy_specID,Q: secrecy_specID] :
% 3.01/1.55 ( ( exprChannel @ X @ ( secrecy_sE @ Secrets ) )
% 3.01/1.55 => ( ~ ( ine @ P @ ( secrecy_sE @ Secrets ) )
% 3.01/1.55 => ( ~ ( ine @ Q @ ( secrecy_sE @ Secrets ) )
% 3.01/1.55 => ( ~ ( member @ secrecy_chanID @ X @ ( ins @ P ) )
% 3.01/1.55 & ~ ( member @ secrecy_chanID @ X @ ( ins @ Q ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_142_LocalSecretsComposition__neg,axiom,
% 3.01/1.55 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 3.01/1.55 ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correc965049635ionLoc @ PQ )
% 3.01/1.55 => ( ( correctCompositionKS @ PQ )
% 3.01/1.55 => ( ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 3.01/1.55 => ( ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) )
% 3.01/1.55 => ( ! [M4: secrecy_Keys] :
% 3.01/1.55 ( ( Ks
% 3.01/1.55 = ( secrecy_kKS @ M4 ) )
% 3.01/1.55 => ( ~ ( ine @ P @ ( secrecy_kE @ M4 ) )
% 3.01/1.55 & ~ ( ine @ Q @ ( secrecy_kE @ M4 ) ) ) )
% 3.01/1.55 => ( ! [M4: secrecy_Secrets] :
% 3.01/1.55 ( ( Ks
% 3.01/1.55 = ( secrecy_sKS @ M4 ) )
% 3.01/1.55 => ( ~ ( ine @ P @ ( secrecy_sE @ M4 ) )
% 3.01/1.55 & ~ ( ine @ Q @ ( secrecy_sE @ M4 ) ) ) )
% 3.01/1.55 => ( ~ ( member @ secrecy_KS @ Ks @ ( sup_sup @ ( set @ secrecy_KS ) @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 3.01/1.55 => ~ ( member @ secrecy_KS @ Ks @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_143_LocalSecretsComposition__neg1,axiom,
% 3.01/1.55 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 3.01/1.55 ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correc965049635ionLoc @ PQ )
% 3.01/1.55 => ( ! [M4: secrecy_Keys] :
% 3.01/1.55 ( ( Ks
% 3.01/1.55 = ( secrecy_kKS @ M4 ) )
% 3.01/1.55 => ( ~ ( ine @ P @ ( secrecy_kE @ M4 ) )
% 3.01/1.55 & ~ ( ine @ Q @ ( secrecy_kE @ M4 ) ) ) )
% 3.01/1.55 => ( ! [M4: secrecy_Secrets] :
% 3.01/1.55 ( ( Ks
% 3.01/1.55 = ( secrecy_sKS @ M4 ) )
% 3.01/1.55 => ( ~ ( ine @ P @ ( secrecy_sE @ M4 ) )
% 3.01/1.55 & ~ ( ine @ Q @ ( secrecy_sE @ M4 ) ) ) )
% 3.01/1.55 => ( ~ ( member @ secrecy_KS @ Ks @ ( localSecrets @ P ) )
% 3.01/1.55 => ( ~ ( member @ secrecy_KS @ Ks @ ( localSecrets @ Q ) )
% 3.01/1.55 => ~ ( member @ secrecy_KS @ Ks @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_144_correctCompositionKS__exprChannel__s__Qex,axiom,
% 3.01/1.55 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 3.01/1.55 ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correctCompositionKS @ PQ )
% 3.01/1.55 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 3.01/1.55 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ Q ) )
% 3.01/1.55 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 3.01/1.55 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 3.01/1.55 => ( ( correctCompositionIn @ PQ )
% 3.01/1.55 => ? [Ch4: secrecy_chanID] :
% 3.01/1.55 ( ( member @ secrecy_chanID @ Ch4 @ ( ins @ PQ ) )
% 3.01/1.55 & ( exprChannel @ Ch4 @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_145_sup__bot_Oright__neutral,axiom,
% 3.01/1.55 ! [A: $tType] :
% 3.01/1.55 ( ( bounde1808546759up_bot @ A )
% 3.01/1.55 => ! [A2: A] :
% 3.01/1.55 ( ( sup_sup @ A @ A2 @ ( bot_bot @ A ) )
% 3.01/1.55 = A2 ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_146_sup__bot_Oneutr__eq__iff,axiom,
% 3.01/1.55 ! [A: $tType] :
% 3.01/1.55 ( ( bounde1808546759up_bot @ A )
% 3.01/1.55 => ! [A2: A,B2: A] :
% 3.01/1.55 ( ( ( bot_bot @ A )
% 3.01/1.55 = ( sup_sup @ A @ A2 @ B2 ) )
% 3.01/1.55 = ( ( A2
% 3.01/1.55 = ( bot_bot @ A ) )
% 3.01/1.55 & ( B2
% 3.01/1.55 = ( bot_bot @ A ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_147_sup__bot_Oleft__neutral,axiom,
% 3.01/1.55 ! [A: $tType] :
% 3.01/1.55 ( ( bounde1808546759up_bot @ A )
% 3.01/1.55 => ! [A2: A] :
% 3.01/1.55 ( ( sup_sup @ A @ ( bot_bot @ A ) @ A2 )
% 3.01/1.55 = A2 ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_148_sup__bot_Oeq__neutr__iff,axiom,
% 3.01/1.55 ! [A: $tType] :
% 3.01/1.55 ( ( bounde1808546759up_bot @ A )
% 3.01/1.55 => ! [A2: A,B2: A] :
% 3.01/1.55 ( ( ( sup_sup @ A @ A2 @ B2 )
% 3.01/1.55 = ( bot_bot @ A ) )
% 3.01/1.55 = ( ( A2
% 3.01/1.55 = ( bot_bot @ A ) )
% 3.01/1.55 & ( B2
% 3.01/1.55 = ( bot_bot @ A ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_149_sup__eq__bot__iff,axiom,
% 3.01/1.55 ! [A: $tType] :
% 3.01/1.55 ( ( bounde1808546759up_bot @ A )
% 3.01/1.55 => ! [X: A,Y2: A] :
% 3.01/1.55 ( ( ( sup_sup @ A @ X @ Y2 )
% 3.01/1.55 = ( bot_bot @ A ) )
% 3.01/1.55 = ( ( X
% 3.01/1.55 = ( bot_bot @ A ) )
% 3.01/1.55 & ( Y2
% 3.01/1.55 = ( bot_bot @ A ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_150_sup__bot__left,axiom,
% 3.01/1.55 ! [A: $tType] :
% 3.01/1.55 ( ( bounde1808546759up_bot @ A )
% 3.01/1.55 => ! [X: A] :
% 3.01/1.55 ( ( sup_sup @ A @ ( bot_bot @ A ) @ X )
% 3.01/1.55 = X ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_151_sup__bot__right,axiom,
% 3.01/1.55 ! [A: $tType] :
% 3.01/1.55 ( ( bounde1808546759up_bot @ A )
% 3.01/1.55 => ! [X: A] :
% 3.01/1.55 ( ( sup_sup @ A @ X @ ( bot_bot @ A ) )
% 3.01/1.55 = X ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_152_bot__eq__sup__iff,axiom,
% 3.01/1.55 ! [A: $tType] :
% 3.01/1.55 ( ( bounde1808546759up_bot @ A )
% 3.01/1.55 => ! [X: A,Y2: A] :
% 3.01/1.55 ( ( ( bot_bot @ A )
% 3.01/1.55 = ( sup_sup @ A @ X @ Y2 ) )
% 3.01/1.55 = ( ( X
% 3.01/1.55 = ( bot_bot @ A ) )
% 3.01/1.55 & ( Y2
% 3.01/1.55 = ( bot_bot @ A ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_153_ineM__Un1,axiom,
% 3.01/1.55 ! [P: secrecy_specID,A3: set @ secrecy_chanID,E: secrecy_Expression,B: set @ secrecy_chanID] :
% 3.01/1.55 ( ( ineM @ P @ A3 @ E )
% 3.01/1.55 => ( ineM @ P @ ( sup_sup @ ( set @ secrecy_chanID ) @ A3 @ B ) @ E ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_154_locStream__def,axiom,
% 3.01/1.55 ( locStream
% 3.01/1.55 = ( ^ [X2: secrecy_specID] :
% 3.01/1.55 ( ^ [Y3: set @ secrecy_chanID,Z: set @ secrecy_chanID] : ( Y3 = Z )
% 3.01/1.55 @ ( loc @ X2 ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_155_inStream__def,axiom,
% 3.01/1.55 ( inStream
% 3.01/1.55 = ( ^ [X2: secrecy_specID] :
% 3.01/1.55 ( ^ [Y3: set @ secrecy_chanID,Z: set @ secrecy_chanID] : ( Y3 = Z )
% 3.01/1.55 @ ( ins @ X2 ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_156_notSpecKeysSecretsExpr__def,axiom,
% 3.01/1.55 ( notSpe1586871396tsExpr
% 3.01/1.55 = ( ^ [P2: secrecy_specID,E3: list @ secrecy_Expression] :
% 3.01/1.55 ( ! [X2: secrecy_Keys] :
% 3.01/1.55 ( ( mem @ secrecy_Expression @ ( secrecy_kE @ X2 ) @ E3 )
% 3.01/1.55 => ~ ( member @ secrecy_KS @ ( secrecy_kKS @ X2 ) @ ( specKeysSecrets @ P2 ) ) )
% 3.01/1.55 & ! [Y4: secrecy_Secrets] :
% 3.01/1.55 ( ( mem @ secrecy_Expression @ ( secrecy_sE @ Y4 ) @ E3 )
% 3.01/1.55 => ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Y4 ) @ ( specKeysSecrets @ P2 ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_157_TBtheorem5a__empty,axiom,
% 3.01/1.55 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.01/1.55 ( ( ( eout @ P @ E )
% 3.01/1.55 | ( eout @ Q @ E ) )
% 3.01/1.55 => ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correc990227761ionOut @ PQ )
% 3.01/1.55 => ( ( ( loc @ PQ )
% 3.01/1.55 = ( bot_bot @ ( set @ secrecy_chanID ) ) )
% 3.01/1.55 => ( eout @ PQ @ E ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_158_correctCompositionKS__subcomp4,axiom,
% 3.01/1.55 ! [C4: secrecy_specID,X: secrecy_specID,Xa: secrecy_Secrets] :
% 3.01/1.55 ( ( correctCompositionKS @ C4 )
% 3.01/1.55 => ( ( member @ secrecy_specID @ X @ ( subcomponents @ C4 ) )
% 3.01/1.55 => ( ( member @ secrecy_Secrets @ Xa @ ( specSecrets @ X ) )
% 3.01/1.55 => ( member @ secrecy_Secrets @ Xa @ ( specSecrets @ C4 ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_159_correctCompositionKS__subcomp3,axiom,
% 3.01/1.55 ! [C4: secrecy_specID,X: secrecy_specID,Xa: secrecy_Keys] :
% 3.01/1.55 ( ( correctCompositionKS @ C4 )
% 3.01/1.55 => ( ( member @ secrecy_specID @ X @ ( subcomponents @ C4 ) )
% 3.01/1.55 => ( ( member @ secrecy_Keys @ Xa @ ( specKeys @ X ) )
% 3.01/1.55 => ( member @ secrecy_Keys @ Xa @ ( specKeys @ C4 ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_160_TBtheorem2a,axiom,
% 3.01/1.55 ! [PQ: secrecy_specID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 3.01/1.55 ( ( eout @ PQ @ E )
% 3.01/1.55 => ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correc990227761ionOut @ PQ )
% 3.01/1.55 => ( ( eout @ P @ E )
% 3.01/1.55 | ( eout @ Q @ E ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_161_correctCompositionKS__subcomp1,axiom,
% 3.01/1.55 ! [C4: secrecy_specID,X: secrecy_specID,Xa: secrecy_Keys] :
% 3.01/1.55 ( ( correctCompositionKS @ C4 )
% 3.01/1.55 => ( ( member @ secrecy_specID @ X @ ( subcomponents @ C4 ) )
% 3.01/1.55 => ( ( member @ secrecy_Keys @ Xa @ ( specKeys @ C4 ) )
% 3.01/1.55 => ? [X3: secrecy_specID] :
% 3.01/1.55 ( ( member @ secrecy_specID @ X3 @ ( subcomponents @ C4 ) )
% 3.01/1.55 & ( member @ secrecy_Keys @ Xa @ ( specKeys @ X3 ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_162_correctCompositionKS__subcomp2,axiom,
% 3.01/1.55 ! [C4: secrecy_specID,X: secrecy_specID,Xa: secrecy_Secrets] :
% 3.01/1.55 ( ( correctCompositionKS @ C4 )
% 3.01/1.55 => ( ( member @ secrecy_specID @ X @ ( subcomponents @ C4 ) )
% 3.01/1.55 => ( ( member @ secrecy_Secrets @ Xa @ ( specSecrets @ C4 ) )
% 3.01/1.55 => ? [X3: secrecy_specID] :
% 3.01/1.55 ( ( member @ secrecy_specID @ X3 @ ( subcomponents @ C4 ) )
% 3.01/1.55 & ( member @ secrecy_Secrets @ Xa @ ( specSecrets @ X3 ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_163_TBtheorem5a__notP1,axiom,
% 3.01/1.55 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.01/1.55 ( ( eout @ P @ E )
% 3.01/1.55 => ( ~ ( eout @ Q @ E )
% 3.01/1.55 => ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correc990227761ionOut @ PQ )
% 3.01/1.55 => ( ? [Ch3: secrecy_chanID] :
% 3.01/1.55 ( ( out_ex985543062Single @ P @ Ch3 @ E )
% 3.01/1.55 & ( member @ secrecy_chanID @ Ch3 @ ( loc @ PQ ) ) )
% 3.01/1.55 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_164_TBtheorem5a__notP2,axiom,
% 3.01/1.55 ! [Q: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set @ secrecy_chanID] :
% 3.01/1.55 ( ~ ( eout @ Q @ E )
% 3.01/1.55 => ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correc990227761ionOut @ PQ )
% 3.01/1.55 => ( ( out_exprChannelSet @ P @ ChSet @ E )
% 3.01/1.55 => ( ! [X3: secrecy_chanID] :
% 3.01/1.55 ( ( member @ secrecy_chanID @ X3 @ ChSet )
% 3.01/1.55 => ( member @ secrecy_chanID @ X3 @ ( loc @ PQ ) ) )
% 3.01/1.55 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_165_TBtheorem5a__notPQ,axiom,
% 3.01/1.55 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set @ secrecy_chanID,E: secrecy_Expression,ChSetQ: set @ secrecy_chanID] :
% 3.01/1.55 ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correc990227761ionOut @ PQ )
% 3.01/1.55 => ( ( out_exprChannelSet @ P @ ChSetP @ E )
% 3.01/1.55 => ( ( out_exprChannelSet @ Q @ ChSetQ @ E )
% 3.01/1.55 => ( ! [X3: secrecy_chanID] :
% 3.01/1.55 ( ( member @ secrecy_chanID @ X3 @ ChSetP )
% 3.01/1.55 => ( member @ secrecy_chanID @ X3 @ ( loc @ PQ ) ) )
% 3.01/1.55 => ( ! [X3: secrecy_chanID] :
% 3.01/1.55 ( ( member @ secrecy_chanID @ X3 @ ChSetQ )
% 3.01/1.55 => ( member @ secrecy_chanID @ X3 @ ( loc @ PQ ) ) )
% 3.01/1.55 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_166_out__exprChannelSet__Single,axiom,
% 3.01/1.55 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 3.01/1.55 ( ( out_exprChannelSet @ P @ ( insert @ secrecy_chanID @ Ch @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ E )
% 3.01/1.55 => ( out_ex985543062Single @ P @ Ch @ E ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_167_out__exprChannelSingle__Set,axiom,
% 3.01/1.55 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 3.01/1.55 ( ( out_ex985543062Single @ P @ Ch @ E )
% 3.01/1.55 => ( out_exprChannelSet @ P @ ( insert @ secrecy_chanID @ Ch @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ E ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_168_TBtheorem5b__notPQ,axiom,
% 3.01/1.55 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set @ secrecy_chanID,E: secrecy_Expression,ChSetQ: set @ secrecy_chanID,M: set @ secrecy_chanID] :
% 3.01/1.55 ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correc990227761ionOut @ PQ )
% 3.01/1.55 => ( ( out_exprChannelSet @ P @ ChSetP @ E )
% 3.01/1.55 => ( ( out_exprChannelSet @ Q @ ChSetQ @ E )
% 3.01/1.55 => ( ( M
% 3.01/1.55 = ( sup_sup @ ( set @ secrecy_chanID ) @ ChSetP @ ChSetQ ) )
% 3.01/1.55 => ( ! [X3: secrecy_chanID] :
% 3.01/1.55 ( ( member @ secrecy_chanID @ X3 @ ChSetP )
% 3.01/1.55 => ( member @ secrecy_chanID @ X3 @ ( loc @ PQ ) ) )
% 3.01/1.55 => ( ! [X3: secrecy_chanID] :
% 3.01/1.55 ( ( member @ secrecy_chanID @ X3 @ ChSetQ )
% 3.01/1.55 => ( member @ secrecy_chanID @ X3 @ ( loc @ PQ ) ) )
% 3.01/1.55 => ~ ( eoutM @ PQ @ M @ E ) ) ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_169_eout__know__s,axiom,
% 3.01/1.55 ! [C4: secrecy_specID,M2: secrecy_Secrets] :
% 3.01/1.55 ( ( knowle1667810483orrect @ C4 @ ( secrecy_sKS @ M2 ) )
% 3.01/1.55 = ( ( eout @ C4 @ ( secrecy_sE @ M2 ) )
% 3.01/1.55 = ( ( member @ secrecy_Secrets @ M2 @ ( specSecrets @ C4 ) )
% 3.01/1.55 | ( knowle1437066798e_know @ C4 @ ( secrecy_sKS @ M2 ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_170_not__know__s__not__eout,axiom,
% 3.01/1.55 ! [M2: secrecy_Secrets,A3: secrecy_specID] :
% 3.01/1.55 ( ~ ( member @ secrecy_Secrets @ M2 @ ( specSecrets @ A3 ) )
% 3.01/1.55 => ( ~ ( knowle1437066798e_know @ A3 @ ( secrecy_sKS @ M2 ) )
% 3.01/1.55 => ( ( knowle1667810483orrect @ A3 @ ( secrecy_sKS @ M2 ) )
% 3.01/1.55 => ~ ( eout @ A3 @ ( secrecy_sE @ M2 ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_171_not__eout__eoutM,axiom,
% 3.01/1.55 ! [P: secrecy_specID,E: secrecy_Expression,M: set @ secrecy_chanID] :
% 3.01/1.55 ( ~ ( eout @ P @ E )
% 3.01/1.55 => ~ ( eoutM @ P @ M @ E ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_172_eoutM__eout,axiom,
% 3.01/1.55 ! [P: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression] :
% 3.01/1.55 ( ( eoutM @ P @ M @ E )
% 3.01/1.55 => ( eout @ P @ E ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_173_TBtheorem2b,axiom,
% 3.01/1.55 ! [PQ: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 3.01/1.55 ( ( eoutM @ PQ @ M @ E )
% 3.01/1.55 => ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correc990227761ionOut @ PQ )
% 3.01/1.55 => ( ( eoutM @ P @ M @ E )
% 3.01/1.55 | ( eoutM @ Q @ M @ E ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_174_TBtheorem5b__notP2,axiom,
% 3.01/1.55 ! [Q: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set @ secrecy_chanID] :
% 3.01/1.55 ( ~ ( eoutM @ Q @ M @ E )
% 3.01/1.55 => ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correc990227761ionOut @ PQ )
% 3.01/1.55 => ( ( out_exprChannelSet @ P @ ChSet @ E )
% 3.01/1.55 => ( ! [X3: secrecy_chanID] :
% 3.01/1.55 ( ( member @ secrecy_chanID @ X3 @ ChSet )
% 3.01/1.55 => ( member @ secrecy_chanID @ X3 @ ( loc @ PQ ) ) )
% 3.01/1.55 => ~ ( eoutM @ PQ @ M @ E ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_175_TBtheorem5b__notP1,axiom,
% 3.01/1.55 ! [P: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.01/1.55 ( ( eoutM @ P @ M @ E )
% 3.01/1.55 => ( ~ ( eoutM @ Q @ M @ E )
% 3.01/1.55 => ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correc990227761ionOut @ PQ )
% 3.01/1.55 => ( ? [Ch3: secrecy_chanID] :
% 3.01/1.55 ( ( out_ex985543062Single @ P @ Ch3 @ E )
% 3.01/1.55 & ( member @ secrecy_chanID @ Ch3 @ M )
% 3.01/1.55 & ( member @ secrecy_chanID @ Ch3 @ ( loc @ PQ ) ) )
% 3.01/1.55 => ~ ( eoutM @ PQ @ M @ E ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_176_eout__know__k,axiom,
% 3.01/1.55 ! [C4: secrecy_specID,M2: secrecy_Keys] :
% 3.01/1.55 ( ( knowle1667810483orrect @ C4 @ ( secrecy_kKS @ M2 ) )
% 3.01/1.55 = ( ( eout @ C4 @ ( secrecy_kE @ M2 ) )
% 3.01/1.55 = ( ( member @ secrecy_Keys @ M2 @ ( specKeys @ C4 ) )
% 3.01/1.55 | ( knowle1437066798e_know @ C4 @ ( secrecy_kKS @ M2 ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_177_not__know__k__not__eout,axiom,
% 3.01/1.55 ! [M2: secrecy_Keys,A3: secrecy_specID] :
% 3.01/1.55 ( ~ ( member @ secrecy_Keys @ M2 @ ( specKeys @ A3 ) )
% 3.01/1.55 => ( ~ ( knowle1437066798e_know @ A3 @ ( secrecy_kKS @ M2 ) )
% 3.01/1.55 => ( ( knowle1667810483orrect @ A3 @ ( secrecy_kKS @ M2 ) )
% 3.01/1.55 => ~ ( eout @ A3 @ ( secrecy_kE @ M2 ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_178_eoutKnowCorrect__L1k,axiom,
% 3.01/1.55 ! [C4: secrecy_specID,M2: secrecy_Keys] :
% 3.01/1.55 ( ( knowle1667810483orrect @ C4 @ ( secrecy_kKS @ M2 ) )
% 3.01/1.55 => ( ( eout @ C4 @ ( secrecy_kE @ M2 ) )
% 3.01/1.55 => ( ( member @ secrecy_Keys @ M2 @ ( specKeys @ C4 ) )
% 3.01/1.55 | ( knowle1437066798e_know @ C4 @ ( secrecy_kKS @ M2 ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_179_eout__know__nonKS__k,axiom,
% 3.01/1.55 ! [M2: secrecy_Keys,A3: secrecy_specID] :
% 3.01/1.55 ( ~ ( member @ secrecy_Keys @ M2 @ ( specKeys @ A3 ) )
% 3.01/1.55 => ( ( eout @ A3 @ ( secrecy_kE @ M2 ) )
% 3.01/1.55 => ( ( knowle1667810483orrect @ A3 @ ( secrecy_kKS @ M2 ) )
% 3.01/1.55 => ( knowle1437066798e_know @ A3 @ ( secrecy_kKS @ M2 ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_180_eout__know__nonKS__s,axiom,
% 3.01/1.55 ! [M2: secrecy_Secrets,A3: secrecy_specID] :
% 3.01/1.55 ( ~ ( member @ secrecy_Secrets @ M2 @ ( specSecrets @ A3 ) )
% 3.01/1.55 => ( ( eout @ A3 @ ( secrecy_sE @ M2 ) )
% 3.01/1.55 => ( ( knowle1667810483orrect @ A3 @ ( secrecy_sKS @ M2 ) )
% 3.01/1.55 => ( knowle1437066798e_know @ A3 @ ( secrecy_sKS @ M2 ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_181_eoutKnowCorrect__L1s,axiom,
% 3.01/1.55 ! [C4: secrecy_specID,M2: secrecy_Secrets] :
% 3.01/1.55 ( ( knowle1667810483orrect @ C4 @ ( secrecy_sKS @ M2 ) )
% 3.01/1.55 => ( ( eout @ C4 @ ( secrecy_sE @ M2 ) )
% 3.01/1.55 => ( ( member @ secrecy_Secrets @ M2 @ ( specSecrets @ C4 ) )
% 3.01/1.55 | ( knowle1437066798e_know @ C4 @ ( secrecy_sKS @ M2 ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_182_TBtheorem5b__PQ,axiom,
% 3.01/1.55 ! [P: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.01/1.55 ( ( ( eoutM @ P @ M @ E )
% 3.01/1.55 | ( eoutM @ Q @ M @ E ) )
% 3.01/1.55 => ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correc990227761ionOut @ PQ )
% 3.01/1.55 => ( ? [Ch3: secrecy_chanID] :
% 3.01/1.55 ( ( ( member @ secrecy_chanID @ Ch3 @ ( out @ P ) )
% 3.01/1.55 | ( member @ secrecy_chanID @ Ch3 @ ( out @ Q ) ) )
% 3.01/1.55 & ( member @ secrecy_chanID @ Ch3 @ M )
% 3.01/1.55 & ( exprChannel @ Ch3 @ E )
% 3.01/1.55 & ~ ( member @ secrecy_chanID @ Ch3 @ ( loc @ PQ ) ) )
% 3.01/1.55 => ( eoutM @ PQ @ M @ E ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_183_TBtheore54b__P,axiom,
% 3.01/1.55 ! [P: secrecy_specID,M: set @ secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 3.01/1.55 ( ( eoutM @ P @ M @ E )
% 3.01/1.55 => ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correc990227761ionOut @ PQ )
% 3.01/1.55 => ( ? [Ch3: secrecy_chanID] :
% 3.01/1.55 ( ( member @ secrecy_chanID @ Ch3 @ ( out @ Q ) )
% 3.01/1.55 & ( exprChannel @ Ch3 @ E )
% 3.01/1.55 & ~ ( member @ secrecy_chanID @ Ch3 @ ( loc @ PQ ) )
% 3.01/1.55 & ( member @ secrecy_chanID @ Ch3 @ M ) )
% 3.01/1.55 => ( eoutM @ PQ @ M @ E ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_184_TBtheorem5a__PQ,axiom,
% 3.01/1.55 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.01/1.55 ( ( ( eout @ P @ E )
% 3.01/1.55 | ( eout @ Q @ E ) )
% 3.01/1.55 => ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correc990227761ionOut @ PQ )
% 3.01/1.55 => ( ? [Ch3: secrecy_chanID] :
% 3.01/1.55 ( ( ( member @ secrecy_chanID @ Ch3 @ ( out @ P ) )
% 3.01/1.55 | ( member @ secrecy_chanID @ Ch3 @ ( out @ Q ) ) )
% 3.01/1.55 & ( exprChannel @ Ch3 @ E )
% 3.01/1.55 & ~ ( member @ secrecy_chanID @ Ch3 @ ( loc @ PQ ) ) )
% 3.01/1.55 => ( eout @ PQ @ E ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_185_eout__def,axiom,
% 3.01/1.55 ( eout
% 3.01/1.55 = ( ^ [SP: secrecy_specID,E2: secrecy_Expression] :
% 3.01/1.55 ? [Ch2: secrecy_chanID] :
% 3.01/1.55 ( ( member @ secrecy_chanID @ Ch2 @ ( out @ SP ) )
% 3.01/1.55 & ( exprChannel @ Ch2 @ E2 ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_186_eoutM__def,axiom,
% 3.01/1.55 ( eoutM
% 3.01/1.55 = ( ^ [SP: secrecy_specID,M3: set @ secrecy_chanID,E2: secrecy_Expression] :
% 3.01/1.55 ? [Ch2: secrecy_chanID] :
% 3.01/1.55 ( ( member @ secrecy_chanID @ Ch2 @ ( out @ SP ) )
% 3.01/1.55 & ( member @ secrecy_chanID @ Ch2 @ M3 )
% 3.01/1.55 & ( exprChannel @ Ch2 @ E2 ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_187_out__exprChannelSet__def,axiom,
% 3.01/1.55 ( out_exprChannelSet
% 3.01/1.55 = ( ^ [SP: secrecy_specID,ChSet2: set @ secrecy_chanID,E2: secrecy_Expression] :
% 3.01/1.55 ( ! [X2: secrecy_chanID] :
% 3.01/1.55 ( ( member @ secrecy_chanID @ X2 @ ChSet2 )
% 3.01/1.55 => ( ( member @ secrecy_chanID @ X2 @ ( out @ SP ) )
% 3.01/1.55 & ( exprChannel @ X2 @ E2 ) ) )
% 3.01/1.55 & ! [X2: secrecy_chanID] :
% 3.01/1.55 ( ( ~ ( member @ secrecy_chanID @ X2 @ ChSet2 )
% 3.01/1.55 & ( member @ secrecy_chanID @ X2 @ ( out @ SP ) ) )
% 3.01/1.55 => ~ ( exprChannel @ X2 @ E2 ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_188_out__exprChannelSingle__def,axiom,
% 3.01/1.55 ( out_ex985543062Single
% 3.01/1.55 = ( ^ [SP: secrecy_specID,Ch2: secrecy_chanID,E2: secrecy_Expression] :
% 3.01/1.55 ( ( member @ secrecy_chanID @ Ch2 @ ( out @ SP ) )
% 3.01/1.55 & ( exprChannel @ Ch2 @ E2 )
% 3.01/1.55 & ! [X2: secrecy_chanID,T: nat] :
% 3.01/1.55 ( ( ( member @ secrecy_chanID @ X2 @ ( out @ SP ) )
% 3.01/1.55 & ( X2 != Ch2 ) )
% 3.01/1.55 => ~ ( exprChannel @ X2 @ E2 ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_189_correctCompositionOut__prop1,axiom,
% 3.01/1.55 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,X: secrecy_chanID] :
% 3.01/1.55 ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correc990227761ionOut @ PQ )
% 3.01/1.55 => ( ( member @ secrecy_chanID @ X @ ( out @ PQ ) )
% 3.01/1.55 => ( ( member @ secrecy_chanID @ X @ ( out @ P ) )
% 3.01/1.55 | ( member @ secrecy_chanID @ X @ ( out @ Q ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_190_TBtheorem45a__P,axiom,
% 3.01/1.55 ! [P: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 3.01/1.55 ( ( eout @ P @ E )
% 3.01/1.55 => ( ( ( subcomponents @ PQ )
% 3.01/1.55 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.01/1.55 => ( ( correc990227761ionOut @ PQ )
% 3.01/1.55 => ( ? [Ch3: secrecy_chanID] :
% 3.01/1.55 ( ( member @ secrecy_chanID @ Ch3 @ ( out @ P ) )
% 3.01/1.55 & ( exprChannel @ Ch3 @ E )
% 3.01/1.55 & ~ ( member @ secrecy_chanID @ Ch3 @ ( loc @ PQ ) ) )
% 3.01/1.55 => ( eout @ PQ @ E ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_191_adv__not__know2,axiom,
% 3.01/1.55 ! [P: secrecy_specID,A3: secrecy_specID,M2: secrecy_Secrets] :
% 3.01/1.55 ( ( ord_less_eq @ ( set @ secrecy_chanID ) @ ( out @ P ) @ ( ins @ A3 ) )
% 3.01/1.55 => ( ~ ( knowle1437066798e_know @ A3 @ ( secrecy_sKS @ M2 ) )
% 3.01/1.55 => ~ ( eout @ P @ ( secrecy_sE @ M2 ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_192_adv__not__know1,axiom,
% 3.01/1.55 ! [P: secrecy_specID,A3: secrecy_specID,M2: secrecy_Keys] :
% 3.01/1.55 ( ( ord_less_eq @ ( set @ secrecy_chanID ) @ ( out @ P ) @ ( ins @ A3 ) )
% 3.01/1.55 => ( ~ ( knowle1437066798e_know @ A3 @ ( secrecy_kKS @ M2 ) )
% 3.01/1.55 => ~ ( eout @ P @ ( secrecy_kE @ M2 ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_193_correctCompositionKeys__subcomp1,axiom,
% 3.01/1.55 ! [C4: secrecy_specID,X: secrecy_specID,Xb: secrecy_Keys] :
% 3.01/1.55 ( ( correc17873122onKeys @ C4 )
% 3.01/1.55 => ( ( member @ secrecy_specID @ X @ ( subcomponents @ C4 ) )
% 3.01/1.55 => ( ( member @ secrecy_Keys @ Xb @ ( specKeys @ C4 ) )
% 3.01/1.55 => ? [X3: secrecy_specID] :
% 3.01/1.55 ( ( member @ secrecy_specID @ X3 @ ( subcomponents @ C4 ) )
% 3.01/1.55 & ( member @ secrecy_Keys @ Xb @ ( specKeys @ X3 ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_194_order__refl,axiom,
% 3.01/1.55 ! [A: $tType] :
% 3.01/1.55 ( ( preorder @ A )
% 3.01/1.55 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_195_subset__antisym,axiom,
% 3.01/1.55 ! [A: $tType,A3: set @ A,B: set @ A] :
% 3.01/1.55 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B )
% 3.01/1.55 => ( ( ord_less_eq @ ( set @ A ) @ B @ A3 )
% 3.01/1.55 => ( A3 = B ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_196_subsetI,axiom,
% 3.01/1.55 ! [A: $tType,A3: set @ A,B: set @ A] :
% 3.01/1.55 ( ! [X3: A] :
% 3.01/1.55 ( ( member @ A @ X3 @ A3 )
% 3.01/1.55 => ( member @ A @ X3 @ B ) )
% 3.01/1.55 => ( ord_less_eq @ ( set @ A ) @ A3 @ B ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_197_empty__subsetI,axiom,
% 3.01/1.55 ! [A: $tType,A3: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A3 ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_198_subset__empty,axiom,
% 3.01/1.55 ! [A: $tType,A3: set @ A] :
% 3.01/1.55 ( ( ord_less_eq @ ( set @ A ) @ A3 @ ( bot_bot @ ( set @ A ) ) )
% 3.01/1.55 = ( A3
% 3.01/1.55 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_199_insert__subset,axiom,
% 3.01/1.55 ! [A: $tType,X: A,A3: set @ A,B: set @ A] :
% 3.01/1.55 ( ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ X @ A3 ) @ B )
% 3.01/1.55 = ( ( member @ A @ X @ B )
% 3.01/1.55 & ( ord_less_eq @ ( set @ A ) @ A3 @ B ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_200_Un__subset__iff,axiom,
% 3.01/1.55 ! [A: $tType,A3: set @ A,B: set @ A,C4: set @ A] :
% 3.01/1.55 ( ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A3 @ B ) @ C4 )
% 3.01/1.55 = ( ( ord_less_eq @ ( set @ A ) @ A3 @ C4 )
% 3.01/1.55 & ( ord_less_eq @ ( set @ A ) @ B @ C4 ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_201_singleton__insert__inj__eq,axiom,
% 3.01/1.55 ! [A: $tType,B2: A,A2: A,A3: set @ A] :
% 3.01/1.55 ( ( ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) )
% 3.01/1.55 = ( insert @ A @ A2 @ A3 ) )
% 3.01/1.55 = ( ( A2 = B2 )
% 3.01/1.55 & ( ord_less_eq @ ( set @ A ) @ A3 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_202_singleton__insert__inj__eq_H,axiom,
% 3.01/1.55 ! [A: $tType,A2: A,A3: set @ A,B2: A] :
% 3.01/1.55 ( ( ( insert @ A @ A2 @ A3 )
% 3.01/1.55 = ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 3.01/1.55 = ( ( A2 = B2 )
% 3.01/1.55 & ( ord_less_eq @ ( set @ A ) @ A3 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_203_subset__singleton__iff,axiom,
% 3.01/1.55 ! [A: $tType,X4: set @ A,A2: A] :
% 3.01/1.55 ( ( ord_less_eq @ ( set @ A ) @ X4 @ ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 3.01/1.55 = ( ( X4
% 3.01/1.55 = ( bot_bot @ ( set @ A ) ) )
% 3.01/1.55 | ( X4
% 3.01/1.55 = ( insert @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_204_subset__singletonD,axiom,
% 3.01/1.55 ! [A: $tType,A3: set @ A,X: A] :
% 3.01/1.55 ( ( ord_less_eq @ ( set @ A ) @ A3 @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 3.01/1.55 => ( ( A3
% 3.01/1.55 = ( bot_bot @ ( set @ A ) ) )
% 3.01/1.55 | ( A3
% 3.01/1.55 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_205_subset__Un__eq,axiom,
% 3.01/1.55 ! [A: $tType] :
% 3.01/1.55 ( ( ord_less_eq @ ( set @ A ) )
% 3.01/1.55 = ( ^ [A4: set @ A,B5: set @ A] :
% 3.01/1.55 ( ( sup_sup @ ( set @ A ) @ A4 @ B5 )
% 3.01/1.55 = B5 ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_206_subset__UnE,axiom,
% 3.01/1.55 ! [A: $tType,C4: set @ A,A3: set @ A,B: set @ A] :
% 3.01/1.55 ( ( ord_less_eq @ ( set @ A ) @ C4 @ ( sup_sup @ ( set @ A ) @ A3 @ B ) )
% 3.01/1.55 => ~ ! [A6: set @ A] :
% 3.01/1.55 ( ( ord_less_eq @ ( set @ A ) @ A6 @ A3 )
% 3.01/1.55 => ! [B6: set @ A] :
% 3.01/1.55 ( ( ord_less_eq @ ( set @ A ) @ B6 @ B )
% 3.01/1.55 => ( C4
% 3.01/1.55 != ( sup_sup @ ( set @ A ) @ A6 @ B6 ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_207_Un__absorb2,axiom,
% 3.01/1.55 ! [A: $tType,B: set @ A,A3: set @ A] :
% 3.01/1.55 ( ( ord_less_eq @ ( set @ A ) @ B @ A3 )
% 3.01/1.55 => ( ( sup_sup @ ( set @ A ) @ A3 @ B )
% 3.01/1.55 = A3 ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_208_Un__absorb1,axiom,
% 3.01/1.55 ! [A: $tType,A3: set @ A,B: set @ A] :
% 3.01/1.55 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B )
% 3.01/1.55 => ( ( sup_sup @ ( set @ A ) @ A3 @ B )
% 3.01/1.55 = B ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_209_Un__upper2,axiom,
% 3.01/1.55 ! [A: $tType,B: set @ A,A3: set @ A] : ( ord_less_eq @ ( set @ A ) @ B @ ( sup_sup @ ( set @ A ) @ A3 @ B ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_210_Un__upper1,axiom,
% 3.01/1.55 ! [A: $tType,A3: set @ A,B: set @ A] : ( ord_less_eq @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ A3 @ B ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_211_Un__least,axiom,
% 3.01/1.55 ! [A: $tType,A3: set @ A,C4: set @ A,B: set @ A] :
% 3.01/1.55 ( ( ord_less_eq @ ( set @ A ) @ A3 @ C4 )
% 3.01/1.55 => ( ( ord_less_eq @ ( set @ A ) @ B @ C4 )
% 3.01/1.55 => ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A3 @ B ) @ C4 ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_212_Un__mono,axiom,
% 3.01/1.55 ! [A: $tType,A3: set @ A,C4: set @ A,B: set @ A,D3: set @ A] :
% 3.01/1.55 ( ( ord_less_eq @ ( set @ A ) @ A3 @ C4 )
% 3.01/1.55 => ( ( ord_less_eq @ ( set @ A ) @ B @ D3 )
% 3.01/1.55 => ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A3 @ B ) @ ( sup_sup @ ( set @ A ) @ C4 @ D3 ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_213_bot_Oextremum__uniqueI,axiom,
% 3.01/1.55 ! [A: $tType] :
% 3.01/1.55 ( ( order_bot @ A )
% 3.01/1.55 => ! [A2: A] :
% 3.01/1.55 ( ( ord_less_eq @ A @ A2 @ ( bot_bot @ A ) )
% 3.01/1.55 => ( A2
% 3.01/1.55 = ( bot_bot @ A ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_214_bot_Oextremum__unique,axiom,
% 3.01/1.55 ! [A: $tType] :
% 3.01/1.55 ( ( order_bot @ A )
% 3.01/1.55 => ! [A2: A] :
% 3.01/1.55 ( ( ord_less_eq @ A @ A2 @ ( bot_bot @ A ) )
% 3.01/1.55 = ( A2
% 3.01/1.55 = ( bot_bot @ A ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_215_bot_Oextremum,axiom,
% 3.01/1.55 ! [A: $tType] :
% 3.01/1.55 ( ( order_bot @ A )
% 3.01/1.55 => ! [A2: A] : ( ord_less_eq @ A @ ( bot_bot @ A ) @ A2 ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_216_subset__insertI2,axiom,
% 3.01/1.55 ! [A: $tType,A3: set @ A,B: set @ A,B2: A] :
% 3.01/1.55 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B )
% 3.01/1.55 => ( ord_less_eq @ ( set @ A ) @ A3 @ ( insert @ A @ B2 @ B ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_217_subset__insertI,axiom,
% 3.01/1.55 ! [A: $tType,B: set @ A,A2: A] : ( ord_less_eq @ ( set @ A ) @ B @ ( insert @ A @ A2 @ B ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_218_subset__insert,axiom,
% 3.01/1.55 ! [A: $tType,X: A,A3: set @ A,B: set @ A] :
% 3.01/1.55 ( ~ ( member @ A @ X @ A3 )
% 3.01/1.55 => ( ( ord_less_eq @ ( set @ A ) @ A3 @ ( insert @ A @ X @ B ) )
% 3.01/1.55 = ( ord_less_eq @ ( set @ A ) @ A3 @ B ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_219_insert__mono,axiom,
% 3.01/1.55 ! [A: $tType,C4: set @ A,D3: set @ A,A2: A] :
% 3.01/1.55 ( ( ord_less_eq @ ( set @ A ) @ C4 @ D3 )
% 3.01/1.55 => ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ A2 @ C4 ) @ ( insert @ A @ A2 @ D3 ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_220_dual__order_Oantisym,axiom,
% 3.01/1.55 ! [A: $tType] :
% 3.01/1.55 ( ( order @ A )
% 3.01/1.55 => ! [B2: A,A2: A] :
% 3.01/1.55 ( ( ord_less_eq @ A @ B2 @ A2 )
% 3.01/1.55 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 3.01/1.55 => ( A2 = B2 ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_221_dual__order_Oeq__iff,axiom,
% 3.01/1.55 ! [A: $tType] :
% 3.01/1.55 ( ( order @ A )
% 3.01/1.55 => ( ( ^ [Y3: A,Z: A] : ( Y3 = Z ) )
% 3.01/1.55 = ( ^ [A5: A,B7: A] :
% 3.01/1.55 ( ( ord_less_eq @ A @ B7 @ A5 )
% 3.01/1.55 & ( ord_less_eq @ A @ A5 @ B7 ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_222_dual__order_Otrans,axiom,
% 3.01/1.55 ! [A: $tType] :
% 3.01/1.55 ( ( order @ A )
% 3.01/1.55 => ! [B2: A,A2: A,C: A] :
% 3.01/1.55 ( ( ord_less_eq @ A @ B2 @ A2 )
% 3.01/1.55 => ( ( ord_less_eq @ A @ C @ B2 )
% 3.01/1.55 => ( ord_less_eq @ A @ C @ A2 ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_223_linorder__wlog,axiom,
% 3.01/1.55 ! [A: $tType] :
% 3.01/1.55 ( ( linorder @ A )
% 3.01/1.55 => ! [P: A > A > $o,A2: A,B2: A] :
% 3.01/1.55 ( ! [A7: A,B8: A] :
% 3.01/1.55 ( ( ord_less_eq @ A @ A7 @ B8 )
% 3.01/1.55 => ( P @ A7 @ B8 ) )
% 3.01/1.55 => ( ! [A7: A,B8: A] :
% 3.01/1.55 ( ( P @ B8 @ A7 )
% 3.01/1.55 => ( P @ A7 @ B8 ) )
% 3.01/1.55 => ( P @ A2 @ B2 ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_224_dual__order_Orefl,axiom,
% 3.01/1.55 ! [A: $tType] :
% 3.01/1.55 ( ( order @ A )
% 3.01/1.55 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_225_order__trans,axiom,
% 3.01/1.55 ! [A: $tType] :
% 3.01/1.55 ( ( preorder @ A )
% 3.01/1.55 => ! [X: A,Y2: A,Z2: A] :
% 3.01/1.55 ( ( ord_less_eq @ A @ X @ Y2 )
% 3.01/1.55 => ( ( ord_less_eq @ A @ Y2 @ Z2 )
% 3.01/1.55 => ( ord_less_eq @ A @ X @ Z2 ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_226_order__class_Oorder_Oantisym,axiom,
% 3.01/1.55 ! [A: $tType] :
% 3.01/1.55 ( ( order @ A )
% 3.01/1.55 => ! [A2: A,B2: A] :
% 3.01/1.55 ( ( ord_less_eq @ A @ A2 @ B2 )
% 3.01/1.55 => ( ( ord_less_eq @ A @ B2 @ A2 )
% 3.01/1.55 => ( A2 = B2 ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_227_ord__le__eq__trans,axiom,
% 3.01/1.55 ! [A: $tType] :
% 3.01/1.55 ( ( ord @ A )
% 3.01/1.55 => ! [A2: A,B2: A,C: A] :
% 3.01/1.55 ( ( ord_less_eq @ A @ A2 @ B2 )
% 3.01/1.55 => ( ( B2 = C )
% 3.01/1.55 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_228_ord__eq__le__trans,axiom,
% 3.01/1.55 ! [A: $tType] :
% 3.01/1.55 ( ( ord @ A )
% 3.01/1.55 => ! [A2: A,B2: A,C: A] :
% 3.01/1.55 ( ( A2 = B2 )
% 3.01/1.55 => ( ( ord_less_eq @ A @ B2 @ C )
% 3.01/1.55 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_229_order__class_Oorder_Oeq__iff,axiom,
% 3.01/1.55 ! [A: $tType] :
% 3.01/1.55 ( ( order @ A )
% 3.01/1.55 => ( ( ^ [Y3: A,Z: A] : ( Y3 = Z ) )
% 3.01/1.55 = ( ^ [A5: A,B7: A] :
% 3.01/1.55 ( ( ord_less_eq @ A @ A5 @ B7 )
% 3.01/1.55 & ( ord_less_eq @ A @ B7 @ A5 ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_230_antisym__conv,axiom,
% 3.01/1.55 ! [A: $tType] :
% 3.01/1.55 ( ( order @ A )
% 3.01/1.55 => ! [Y2: A,X: A] :
% 3.01/1.55 ( ( ord_less_eq @ A @ Y2 @ X )
% 3.01/1.55 => ( ( ord_less_eq @ A @ X @ Y2 )
% 3.01/1.55 = ( X = Y2 ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_231_le__cases3,axiom,
% 3.01/1.55 ! [A: $tType] :
% 3.01/1.55 ( ( linorder @ A )
% 3.01/1.55 => ! [X: A,Y2: A,Z2: A] :
% 3.01/1.55 ( ( ( ord_less_eq @ A @ X @ Y2 )
% 3.01/1.55 => ~ ( ord_less_eq @ A @ Y2 @ Z2 ) )
% 3.01/1.55 => ( ( ( ord_less_eq @ A @ Y2 @ X )
% 3.01/1.55 => ~ ( ord_less_eq @ A @ X @ Z2 ) )
% 3.01/1.55 => ( ( ( ord_less_eq @ A @ X @ Z2 )
% 3.01/1.55 => ~ ( ord_less_eq @ A @ Z2 @ Y2 ) )
% 3.01/1.55 => ( ( ( ord_less_eq @ A @ Z2 @ Y2 )
% 3.01/1.55 => ~ ( ord_less_eq @ A @ Y2 @ X ) )
% 3.01/1.55 => ( ( ( ord_less_eq @ A @ Y2 @ Z2 )
% 3.01/1.55 => ~ ( ord_less_eq @ A @ Z2 @ X ) )
% 3.01/1.55 => ~ ( ( ord_less_eq @ A @ Z2 @ X )
% 3.01/1.55 => ~ ( ord_less_eq @ A @ X @ Y2 ) ) ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_232_order_Otrans,axiom,
% 3.01/1.55 ! [A: $tType] :
% 3.01/1.55 ( ( order @ A )
% 3.01/1.55 => ! [A2: A,B2: A,C: A] :
% 3.01/1.55 ( ( ord_less_eq @ A @ A2 @ B2 )
% 3.01/1.55 => ( ( ord_less_eq @ A @ B2 @ C )
% 3.01/1.55 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_233_le__cases,axiom,
% 3.01/1.55 ! [A: $tType] :
% 3.01/1.55 ( ( linorder @ A )
% 3.01/1.55 => ! [X: A,Y2: A] :
% 3.01/1.55 ( ~ ( ord_less_eq @ A @ X @ Y2 )
% 3.01/1.55 => ( ord_less_eq @ A @ Y2 @ X ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_234_eq__refl,axiom,
% 3.01/1.55 ! [A: $tType] :
% 3.01/1.55 ( ( preorder @ A )
% 3.01/1.55 => ! [X: A,Y2: A] :
% 3.01/1.55 ( ( X = Y2 )
% 3.01/1.55 => ( ord_less_eq @ A @ X @ Y2 ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_235_linear,axiom,
% 3.01/1.55 ! [A: $tType] :
% 3.01/1.55 ( ( linorder @ A )
% 3.01/1.55 => ! [X: A,Y2: A] :
% 3.01/1.55 ( ( ord_less_eq @ A @ X @ Y2 )
% 3.01/1.55 | ( ord_less_eq @ A @ Y2 @ X ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_236_antisym,axiom,
% 3.01/1.55 ! [A: $tType] :
% 3.01/1.55 ( ( order @ A )
% 3.01/1.55 => ! [X: A,Y2: A] :
% 3.01/1.55 ( ( ord_less_eq @ A @ X @ Y2 )
% 3.01/1.55 => ( ( ord_less_eq @ A @ Y2 @ X )
% 3.01/1.55 => ( X = Y2 ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_237_eq__iff,axiom,
% 3.01/1.55 ! [A: $tType] :
% 3.01/1.55 ( ( order @ A )
% 3.01/1.55 => ( ( ^ [Y3: A,Z: A] : ( Y3 = Z ) )
% 3.01/1.55 = ( ^ [X2: A,Y4: A] :
% 3.01/1.55 ( ( ord_less_eq @ A @ X2 @ Y4 )
% 3.01/1.55 & ( ord_less_eq @ A @ Y4 @ X2 ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_238_ord__le__eq__subst,axiom,
% 3.01/1.55 ! [A: $tType,B3: $tType] :
% 3.01/1.55 ( ( ( ord @ B3 )
% 3.01/1.55 & ( ord @ A ) )
% 3.01/1.55 => ! [A2: A,B2: A,F: A > B3,C: B3] :
% 3.01/1.55 ( ( ord_less_eq @ A @ A2 @ B2 )
% 3.01/1.55 => ( ( ( F @ B2 )
% 3.01/1.55 = C )
% 3.01/1.55 => ( ! [X3: A,Y: A] :
% 3.01/1.55 ( ( ord_less_eq @ A @ X3 @ Y )
% 3.01/1.55 => ( ord_less_eq @ B3 @ ( F @ X3 ) @ ( F @ Y ) ) )
% 3.01/1.55 => ( ord_less_eq @ B3 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_239_ord__eq__le__subst,axiom,
% 3.01/1.55 ! [A: $tType,B3: $tType] :
% 3.01/1.55 ( ( ( ord @ B3 )
% 3.01/1.55 & ( ord @ A ) )
% 3.01/1.55 => ! [A2: A,F: B3 > A,B2: B3,C: B3] :
% 3.01/1.55 ( ( A2
% 3.01/1.55 = ( F @ B2 ) )
% 3.01/1.55 => ( ( ord_less_eq @ B3 @ B2 @ C )
% 3.01/1.55 => ( ! [X3: B3,Y: B3] :
% 3.01/1.55 ( ( ord_less_eq @ B3 @ X3 @ Y )
% 3.01/1.55 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y ) ) )
% 3.01/1.55 => ( ord_less_eq @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_240_order__subst2,axiom,
% 3.01/1.55 ! [A: $tType,C2: $tType] :
% 3.01/1.55 ( ( ( order @ C2 )
% 3.01/1.55 & ( order @ A ) )
% 3.01/1.55 => ! [A2: A,B2: A,F: A > C2,C: C2] :
% 3.01/1.55 ( ( ord_less_eq @ A @ A2 @ B2 )
% 3.01/1.55 => ( ( ord_less_eq @ C2 @ ( F @ B2 ) @ C )
% 3.01/1.55 => ( ! [X3: A,Y: A] :
% 3.01/1.55 ( ( ord_less_eq @ A @ X3 @ Y )
% 3.01/1.55 => ( ord_less_eq @ C2 @ ( F @ X3 ) @ ( F @ Y ) ) )
% 3.01/1.55 => ( ord_less_eq @ C2 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_241_order__subst1,axiom,
% 3.01/1.55 ! [A: $tType,B3: $tType] :
% 3.01/1.55 ( ( ( order @ B3 )
% 3.01/1.55 & ( order @ A ) )
% 3.01/1.55 => ! [A2: A,F: B3 > A,B2: B3,C: B3] :
% 3.01/1.55 ( ( ord_less_eq @ A @ A2 @ ( F @ B2 ) )
% 3.01/1.55 => ( ( ord_less_eq @ B3 @ B2 @ C )
% 3.01/1.55 => ( ! [X3: B3,Y: B3] :
% 3.01/1.55 ( ( ord_less_eq @ B3 @ X3 @ Y )
% 3.01/1.55 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y ) ) )
% 3.01/1.55 => ( ord_less_eq @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_242_Collect__mono__iff,axiom,
% 3.01/1.55 ! [A: $tType,P: A > $o,Q: A > $o] :
% 3.01/1.55 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 3.01/1.55 = ( ! [X2: A] :
% 3.01/1.55 ( ( P @ X2 )
% 3.01/1.55 => ( Q @ X2 ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_243_le__fun__def,axiom,
% 3.01/1.55 ! [B3: $tType,A: $tType] :
% 3.01/1.55 ( ( ord @ B3 )
% 3.01/1.55 => ( ( ord_less_eq @ ( A > B3 ) )
% 3.01/1.55 = ( ^ [F2: A > B3,G2: A > B3] :
% 3.01/1.55 ! [X2: A] : ( ord_less_eq @ B3 @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_244_set__eq__subset,axiom,
% 3.01/1.55 ! [A: $tType] :
% 3.01/1.55 ( ( ^ [Y3: set @ A,Z: set @ A] : ( Y3 = Z ) )
% 3.01/1.55 = ( ^ [A4: set @ A,B5: set @ A] :
% 3.01/1.55 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 3.01/1.55 & ( ord_less_eq @ ( set @ A ) @ B5 @ A4 ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_245_le__funI,axiom,
% 3.01/1.55 ! [B3: $tType,A: $tType] :
% 3.01/1.55 ( ( ord @ B3 )
% 3.01/1.55 => ! [F: A > B3,G: A > B3] :
% 3.01/1.55 ( ! [X3: A] : ( ord_less_eq @ B3 @ ( F @ X3 ) @ ( G @ X3 ) )
% 3.01/1.55 => ( ord_less_eq @ ( A > B3 ) @ F @ G ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_246_le__funE,axiom,
% 3.01/1.55 ! [B3: $tType,A: $tType] :
% 3.01/1.55 ( ( ord @ B3 )
% 3.01/1.55 => ! [F: A > B3,G: A > B3,X: A] :
% 3.01/1.55 ( ( ord_less_eq @ ( A > B3 ) @ F @ G )
% 3.01/1.55 => ( ord_less_eq @ B3 @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_247_le__funD,axiom,
% 3.01/1.55 ! [B3: $tType,A: $tType] :
% 3.01/1.55 ( ( ord @ B3 )
% 3.01/1.55 => ! [F: A > B3,G: A > B3,X: A] :
% 3.01/1.55 ( ( ord_less_eq @ ( A > B3 ) @ F @ G )
% 3.01/1.55 => ( ord_less_eq @ B3 @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_248_subset__trans,axiom,
% 3.01/1.55 ! [A: $tType,A3: set @ A,B: set @ A,C4: set @ A] :
% 3.01/1.55 ( ( ord_less_eq @ ( set @ A ) @ A3 @ B )
% 3.01/1.55 => ( ( ord_less_eq @ ( set @ A ) @ B @ C4 )
% 3.01/1.55 => ( ord_less_eq @ ( set @ A ) @ A3 @ C4 ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_249_Collect__mono,axiom,
% 3.01/1.55 ! [A: $tType,P: A > $o,Q: A > $o] :
% 3.01/1.55 ( ! [X3: A] :
% 3.01/1.55 ( ( P @ X3 )
% 3.01/1.55 => ( Q @ X3 ) )
% 3.01/1.55 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_250_subset__refl,axiom,
% 3.01/1.55 ! [A: $tType,A3: set @ A] : ( ord_less_eq @ ( set @ A ) @ A3 @ A3 ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_251_subset__iff,axiom,
% 3.01/1.55 ! [A: $tType] :
% 3.01/1.55 ( ( ord_less_eq @ ( set @ A ) )
% 3.01/1.55 = ( ^ [A4: set @ A,B5: set @ A] :
% 3.01/1.55 ! [T: A] :
% 3.01/1.55 ( ( member @ A @ T @ A4 )
% 3.01/1.55 => ( member @ A @ T @ B5 ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_252_equalityD2,axiom,
% 3.01/1.55 ! [A: $tType,A3: set @ A,B: set @ A] :
% 3.01/1.55 ( ( A3 = B )
% 3.01/1.55 => ( ord_less_eq @ ( set @ A ) @ B @ A3 ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_253_equalityD1,axiom,
% 3.01/1.55 ! [A: $tType,A3: set @ A,B: set @ A] :
% 3.01/1.55 ( ( A3 = B )
% 3.01/1.55 => ( ord_less_eq @ ( set @ A ) @ A3 @ B ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_254_subset__eq,axiom,
% 3.01/1.55 ! [A: $tType] :
% 3.01/1.55 ( ( ord_less_eq @ ( set @ A ) )
% 3.01/1.55 = ( ^ [A4: set @ A,B5: set @ A] :
% 3.01/1.55 ! [X2: A] :
% 3.01/1.55 ( ( member @ A @ X2 @ A4 )
% 3.01/1.55 => ( member @ A @ X2 @ B5 ) ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(fact_255_equalityE,axiom,
% 3.01/1.55 ! [A: $tType,A3: set @ A,B: set @ A] :
% 3.01/1.55 ( ( A3 = B )
% 3.01/1.55 => ~ ( ( ord_less_eq @ ( set @ A ) @ A3 @ B )
% 3.01/1.55 => ~ ( ord_less_eq @ ( set @ A ) @ B @ A3 ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(tcon_HOL_Obool___Lattices_Obounded__lattice,axiom,
% 3.01/1.55 bounded_lattice @ $o ).
% 3.01/1.55
% 3.01/1.55 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1,axiom,
% 3.01/1.55 ! [A8: $tType] : ( bounded_lattice @ ( set @ A8 ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(tcon_fun___Lattices_Obounded__lattice_2,axiom,
% 3.01/1.55 ! [A8: $tType,A9: $tType] :
% 3.01/1.55 ( ( bounded_lattice @ A9 )
% 3.01/1.55 => ( bounded_lattice @ ( A8 > A9 ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(tcon_fun___Lattices_Obounded__semilattice__sup__bot,axiom,
% 3.01/1.55 ! [A8: $tType,A9: $tType] :
% 3.01/1.55 ( ( bounded_lattice @ A9 )
% 3.01/1.55 => ( bounde1808546759up_bot @ ( A8 > A9 ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(tcon_fun___Orderings_Oorder__bot,axiom,
% 3.01/1.55 ! [A8: $tType,A9: $tType] :
% 3.01/1.55 ( ( order_bot @ A9 )
% 3.01/1.55 => ( order_bot @ ( A8 > A9 ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(tcon_fun___Orderings_Opreorder,axiom,
% 3.01/1.55 ! [A8: $tType,A9: $tType] :
% 3.01/1.55 ( ( preorder @ A9 )
% 3.01/1.55 => ( preorder @ ( A8 > A9 ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(tcon_fun___Orderings_Oorder,axiom,
% 3.01/1.55 ! [A8: $tType,A9: $tType] :
% 3.01/1.55 ( ( order @ A9 )
% 3.01/1.55 => ( order @ ( A8 > A9 ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(tcon_fun___Orderings_Oord,axiom,
% 3.01/1.55 ! [A8: $tType,A9: $tType] :
% 3.01/1.55 ( ( ord @ A9 )
% 3.01/1.55 => ( ord @ ( A8 > A9 ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(tcon_fun___Orderings_Obot,axiom,
% 3.01/1.55 ! [A8: $tType,A9: $tType] :
% 3.01/1.55 ( ( bot @ A9 )
% 3.01/1.55 => ( bot @ ( A8 > A9 ) ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(tcon_Nat_Onat___Orderings_Oorder__bot_3,axiom,
% 3.01/1.55 order_bot @ nat ).
% 3.01/1.55
% 3.01/1.55 thf(tcon_Nat_Onat___Orderings_Opreorder_4,axiom,
% 3.01/1.55 preorder @ nat ).
% 3.01/1.55
% 3.01/1.55 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 3.01/1.55 linorder @ nat ).
% 3.01/1.55
% 3.01/1.55 thf(tcon_Nat_Onat___Orderings_Oorder_5,axiom,
% 3.01/1.55 order @ nat ).
% 3.01/1.55
% 3.01/1.55 thf(tcon_Nat_Onat___Orderings_Oord_6,axiom,
% 3.01/1.55 ord @ nat ).
% 3.01/1.55
% 3.01/1.55 thf(tcon_Nat_Onat___Orderings_Obot_7,axiom,
% 3.01/1.55 bot @ nat ).
% 3.01/1.55
% 3.01/1.55 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_8,axiom,
% 3.01/1.55 ! [A8: $tType] : ( bounde1808546759up_bot @ ( set @ A8 ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(tcon_Set_Oset___Orderings_Oorder__bot_9,axiom,
% 3.01/1.55 ! [A8: $tType] : ( order_bot @ ( set @ A8 ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(tcon_Set_Oset___Orderings_Opreorder_10,axiom,
% 3.01/1.55 ! [A8: $tType] : ( preorder @ ( set @ A8 ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(tcon_Set_Oset___Orderings_Oorder_11,axiom,
% 3.01/1.55 ! [A8: $tType] : ( order @ ( set @ A8 ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(tcon_Set_Oset___Orderings_Oord_12,axiom,
% 3.01/1.55 ! [A8: $tType] : ( ord @ ( set @ A8 ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(tcon_Set_Oset___Orderings_Obot_13,axiom,
% 3.01/1.55 ! [A8: $tType] : ( bot @ ( set @ A8 ) ) ).
% 3.01/1.55
% 3.01/1.55 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_14,axiom,
% 3.01/1.55 bounde1808546759up_bot @ $o ).
% 3.01/1.55
% 3.01/1.55 thf(tcon_HOL_Obool___Orderings_Oorder__bot_15,axiom,
% 3.01/1.55 order_bot @ $o ).
% 3.01/1.55
% 3.01/1.55 thf(tcon_HOL_Obool___Orderings_Opreorder_16,axiom,
% 3.01/1.55 preorder @ $o ).
% 3.01/1.55
% 3.01/1.55 thf(tcon_HOL_Obool___Orderings_Olinorder_17,axiom,
% 3.01/1.55 linorder @ $o ).
% 3.01/1.55
% 3.01/1.55 thf(tcon_HOL_Obool___Orderings_Oorder_18,axiom,
% 3.01/1.55 order @ $o ).
% 3.01/1.55
% 3.01/1.55 thf(tcon_HOL_Obool___Orderings_Oord_19,axiom,
% 3.01/1.55 ord @ $o ).
% 3.01/1.55
% 3.01/1.55 thf(tcon_HOL_Obool___Orderings_Obot_20,axiom,
% 3.01/1.55 bot @ $o ).
% 3.01/1.55
% 3.01/1.55 thf(conj_0,conjecture,
% 3.01/1.55 ~ ( member @ secrecy_KS @ m @ ( specKeysSecrets @ pq ) ) ).
% 3.01/1.55 ------------------------
% 3.01/1.58 % (5203)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_5010 for (2999ds/183Mi)
% 3.01/1.58 % (5207)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_5010 for (2999ds/2Mi)
% 3.01/1.58 % (5208)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_5010 for (2999ds/275Mi)
% 3.01/1.58 % (5207)Instruction limit reached!
% 3.01/1.58 % (5207)------------------------------
% 3.01/1.58 % (5207)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.01/1.58 % (5207)Termination reason: Unknown
% 3.01/1.58 % (5207)Termination phase: shuffling
% 3.01/1.58
% 3.01/1.58 % (5207)Memory used [KB]: 1407
% 3.01/1.58 % (5207)Time elapsed: 0.002 s
% 3.01/1.58 % (5207)Instructions burned: 3 (million)
% 3.01/1.58 % (5207)------------------------------
% 3.01/1.58 % (5207)------------------------------
% 3.01/1.58 % (5206)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_5010 for (2999ds/2Mi)
% 3.01/1.58 % (5206)Instruction limit reached!
% 3.01/1.58 % (5206)------------------------------
% 3.01/1.58 % (5206)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.01/1.58 % (5206)Termination reason: Unknown
% 3.01/1.58 % (5206)Termination phase: shuffling
% 3.01/1.58
% 3.01/1.58 % (5206)Memory used [KB]: 1279
% 3.01/1.58 % (5206)Time elapsed: 0.003 s
% 3.01/1.58 % (5206)Instructions burned: 2 (million)
% 3.01/1.58 % (5206)------------------------------
% 3.01/1.58 % (5206)------------------------------
% 3.01/1.58 % (5205)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_5010 for (2999ds/27Mi)
% 3.01/1.58 % (5209)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_5010 for (2999ds/18Mi)
% 3.01/1.58 % (5204)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_5010 for (2999ds/4Mi)
% 3.01/1.58 % (5204)Instruction limit reached!
% 3.01/1.58 % (5204)------------------------------
% 3.01/1.58 % (5204)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.01/1.58 % (5204)Termination reason: Unknown
% 3.01/1.58 % (5204)Termination phase: shuffling
% 3.01/1.58
% 3.01/1.58 % (5204)Memory used [KB]: 1407
% 3.01/1.58 % (5204)Time elapsed: 0.003 s
% 3.01/1.58 % (5204)Instructions burned: 6 (million)
% 3.01/1.58 % (5204)------------------------------
% 3.01/1.58 % (5204)------------------------------
% 3.01/1.59 % (5210)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_5010 for (2999ds/3Mi)
% 3.01/1.59 % (5210)Instruction limit reached!
% 3.01/1.59 % (5210)------------------------------
% 3.01/1.59 % (5210)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.01/1.59 % (5210)Termination reason: Unknown
% 3.01/1.59 % (5210)Termination phase: shuffling
% 3.01/1.59
% 3.01/1.59 % (5210)Memory used [KB]: 1407
% 3.01/1.59 % (5210)Time elapsed: 0.002 s
% 3.01/1.59 % (5210)Instructions burned: 3 (million)
% 3.01/1.59 % (5210)------------------------------
% 3.01/1.59 % (5210)------------------------------
% 3.01/1.59 % (5205)Instruction limit reached!
% 3.01/1.59 % (5205)------------------------------
% 3.01/1.59 % (5205)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.01/1.59 % (5205)Termination reason: Unknown
% 3.01/1.59 % (5205)Termination phase: shuffling
% 3.01/1.59
% 3.01/1.59 % (5205)Memory used [KB]: 1918
% 3.01/1.59 % (5205)Time elapsed: 0.011 s
% 3.01/1.59 % (5205)Instructions burned: 29 (million)
% 3.01/1.59 % (5205)------------------------------
% 3.01/1.59 % (5205)------------------------------
% 3.01/1.59 % (5209)Instruction limit reached!
% 3.01/1.59 % (5209)------------------------------
% 3.01/1.59 % (5209)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.01/1.59 % (5209)Termination reason: Unknown
% 3.01/1.59 % (5209)Termination phase: shuffling
% 3.01/1.59
% 3.01/1.59 % (5209)Memory used [KB]: 1663
% 3.01/1.59 % (5209)Time elapsed: 0.011 s
% 3.01/1.59 % (5209)Instructions burned: 19 (million)
% 3.01/1.59 % (5209)------------------------------
% 3.01/1.59 % (5209)------------------------------
% 3.01/1.59 % (5211)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_5010 for (2999ds/37Mi)
% 3.01/1.59 % (5212)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_5010 for (2999ds/15Mi)
% 3.08/1.60 % (5213)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_5010 for (2999ds/3Mi)
% 3.08/1.60 % (5213)Instruction limit reached!
% 3.08/1.60 % (5213)------------------------------
% 3.08/1.60 % (5213)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.60 % (5213)Termination reason: Unknown
% 3.08/1.60 % (5213)Termination phase: shuffling
% 3.08/1.60
% 3.08/1.60 % (5213)Memory used [KB]: 1407
% 3.08/1.60 % (5213)Time elapsed: 0.002 s
% 3.08/1.60 % (5213)Instructions burned: 3 (million)
% 3.08/1.60 % (5213)------------------------------
% 3.08/1.60 % (5213)------------------------------
% 3.08/1.60 % (5212)Instruction limit reached!
% 3.08/1.60 % (5212)------------------------------
% 3.08/1.60 % (5212)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.60 % (5212)Termination reason: Unknown
% 3.08/1.60 % (5212)Termination phase: shuffling
% 3.08/1.60
% 3.08/1.60 % (5212)Memory used [KB]: 1535
% 3.08/1.60 % (5212)Time elapsed: 0.008 s
% 3.08/1.60 % (5212)Instructions burned: 17 (million)
% 3.08/1.60 % (5212)------------------------------
% 3.08/1.60 % (5212)------------------------------
% 3.08/1.60 % (5208)Refutation not found, incomplete strategy
% 3.08/1.60 % (5208)------------------------------
% 3.08/1.60 % (5208)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.60 % (5208)Termination reason: Refutation not found, incomplete strategy
% 3.08/1.60
% 3.08/1.60
% 3.08/1.60 % (5208)Memory used [KB]: 6524
% 3.08/1.60 % (5208)Time elapsed: 0.023 s
% 3.08/1.60 % (5208)Instructions burned: 67 (million)
% 3.08/1.60 % (5208)------------------------------
% 3.08/1.60 % (5208)------------------------------
% 3.08/1.60 % (5214)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_5010 for (2999ds/1041Mi)
% 3.08/1.60 % (5215)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_5010 for (2999ds/7Mi)
% 3.08/1.60 % (5211)Instruction limit reached!
% 3.08/1.60 % (5211)------------------------------
% 3.08/1.60 % (5211)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.60 % (5211)Termination reason: Unknown
% 3.08/1.60 % (5211)Termination phase: shuffling
% 3.08/1.60
% 3.08/1.60 % (5211)Memory used [KB]: 2046
% 3.08/1.60 % (5211)Time elapsed: 0.013 s
% 3.08/1.60 % (5211)Instructions burned: 38 (million)
% 3.08/1.60 % (5211)------------------------------
% 3.08/1.60 % (5211)------------------------------
% 3.08/1.60 % (5215)Instruction limit reached!
% 3.08/1.60 % (5215)------------------------------
% 3.08/1.60 % (5215)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.60 % (5215)Termination reason: Unknown
% 3.08/1.60 % (5215)Termination phase: shuffling
% 3.08/1.60
% 3.08/1.60 % (5215)Memory used [KB]: 1407
% 3.08/1.60 % (5215)Time elapsed: 0.004 s
% 3.08/1.60 % (5215)Instructions burned: 8 (million)
% 3.08/1.60 % (5215)------------------------------
% 3.08/1.60 % (5215)------------------------------
% 3.08/1.61 % (5216)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_5010 for (2999ds/16Mi)
% 3.08/1.61 % (5218)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_5010 for (2999ds/3Mi)
% 3.08/1.61 % (5218)Instruction limit reached!
% 3.08/1.61 % (5218)------------------------------
% 3.08/1.61 % (5218)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.61 % (5218)Termination reason: Unknown
% 3.08/1.61 % (5218)Termination phase: shuffling
% 3.08/1.61
% 3.08/1.61 % (5218)Memory used [KB]: 1407
% 3.08/1.61 % (5218)Time elapsed: 0.003 s
% 3.08/1.61 % (5218)Instructions burned: 3 (million)
% 3.08/1.61 % (5218)------------------------------
% 3.08/1.61 % (5218)------------------------------
% 3.08/1.61 % (5217)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_5010 for (2999ds/3Mi)
% 3.08/1.61 % (5219)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_5010 for (2999ds/7Mi)
% 3.08/1.61 % (5216)Instruction limit reached!
% 3.08/1.61 % (5216)------------------------------
% 3.08/1.61 % (5216)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.61 % (5216)Termination reason: Unknown
% 3.08/1.61 % (5216)Termination phase: shuffling
% 3.08/1.61
% 3.08/1.61 % (5216)Memory used [KB]: 1663
% 3.08/1.61 % (5216)Time elapsed: 0.007 s
% 3.08/1.61 % (5216)Instructions burned: 18 (million)
% 3.08/1.61 % (5216)------------------------------
% 3.08/1.61 % (5216)------------------------------
% 3.08/1.62 % (5220)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_5010 for (2999ds/3Mi)
% 3.08/1.62 % (5217)Instruction limit reached!
% 3.08/1.62 % (5217)------------------------------
% 3.08/1.62 % (5217)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.62 % (5217)Termination reason: Unknown
% 3.08/1.62 % (5217)Termination phase: shuffling
% 3.08/1.62
% 3.08/1.62 % (5217)Memory used [KB]: 1407
% 3.08/1.62 % (5217)Time elapsed: 0.004 s
% 3.08/1.62 % (5217)Instructions burned: 4 (million)
% 3.08/1.62 % (5217)------------------------------
% 3.08/1.62 % (5217)------------------------------
% 3.08/1.62 % (5220)Instruction limit reached!
% 3.08/1.62 % (5220)------------------------------
% 3.08/1.62 % (5220)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.62 % (5220)Termination reason: Unknown
% 3.08/1.62 % (5220)Termination phase: shuffling
% 3.08/1.62
% 3.08/1.62 % (5220)Memory used [KB]: 1407
% 3.08/1.62 % (5220)Time elapsed: 0.002 s
% 3.08/1.62 % (5220)Instructions burned: 4 (million)
% 3.08/1.62 % (5220)------------------------------
% 3.08/1.62 % (5220)------------------------------
% 3.08/1.62 % (5219)Instruction limit reached!
% 3.08/1.62 % (5219)------------------------------
% 3.08/1.62 % (5219)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.62 % (5219)Termination reason: Unknown
% 3.08/1.62 % (5219)Termination phase: shuffling
% 3.08/1.62
% 3.08/1.62 % (5219)Memory used [KB]: 1535
% 3.08/1.62 % (5219)Time elapsed: 0.004 s
% 3.08/1.62 % (5219)Instructions burned: 8 (million)
% 3.08/1.62 % (5219)------------------------------
% 3.08/1.62 % (5219)------------------------------
% 3.08/1.62 % (5221)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_5010 for (2999ds/4Mi)
% 3.08/1.62 % (5222)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_5010 for (2999ds/18Mi)
% 3.08/1.62 % (5221)Instruction limit reached!
% 3.08/1.62 % (5221)------------------------------
% 3.08/1.62 % (5221)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.62 % (5221)Termination reason: Unknown
% 3.08/1.62 % (5221)Termination phase: shuffling
% 3.08/1.62
% 3.08/1.62 % (5221)Memory used [KB]: 1407
% 3.08/1.62 % (5221)Time elapsed: 0.003 s
% 3.08/1.62 % (5221)Instructions burned: 6 (million)
% 3.08/1.62 % (5221)------------------------------
% 3.08/1.62 % (5221)------------------------------
% 3.08/1.63 % (5224)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_5010 for (2999ds/6Mi)
% 3.08/1.63 % (5225)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_5010 for (2999ds/902Mi)
% 3.08/1.63 % (5224)Instruction limit reached!
% 3.08/1.63 % (5224)------------------------------
% 3.08/1.63 % (5224)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.63 % (5224)Termination reason: Unknown
% 3.08/1.63 % (5224)Termination phase: shuffling
% 3.08/1.63
% 3.08/1.63 % (5224)Memory used [KB]: 1407
% 3.08/1.63 % (5224)Time elapsed: 0.004 s
% 3.08/1.63 % (5224)Instructions burned: 8 (million)
% 3.08/1.63 % (5224)------------------------------
% 3.08/1.63 % (5224)------------------------------
% 3.08/1.63 % (5222)Instruction limit reached!
% 3.08/1.63 % (5222)------------------------------
% 3.08/1.63 % (5222)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.63 % (5222)Termination reason: Unknown
% 3.08/1.63 % (5222)Termination phase: shuffling
% 3.08/1.63
% 3.08/1.63 % (5222)Memory used [KB]: 1663
% 3.08/1.63 % (5222)Time elapsed: 0.008 s
% 3.08/1.63 % (5222)Instructions burned: 20 (million)
% 3.08/1.63 % (5222)------------------------------
% 3.08/1.63 % (5222)------------------------------
% 3.08/1.63 % (5223)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_5010 for (2999ds/710Mi)
% 3.08/1.63 % (5226)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_5010 for (2999ds/21Mi)
% 3.08/1.64 % (5203)Instruction limit reached!
% 3.08/1.64 % (5203)------------------------------
% 3.08/1.64 % (5203)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.64 % (5203)Termination reason: Unknown
% 3.08/1.64 % (5203)Termination phase: Saturation
% 3.08/1.64
% 3.08/1.64 % (5203)Memory used [KB]: 6908
% 3.08/1.64 % (5203)Time elapsed: 0.061 s
% 3.08/1.64 % (5203)Instructions burned: 183 (million)
% 3.08/1.64 % (5203)------------------------------
% 3.08/1.64 % (5203)------------------------------
% 3.08/1.64 % (5227)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_5010 for (2999ds/5Mi)
% 3.08/1.64 % (5228)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_5010 for (2999ds/6Mi)
% 3.08/1.64 % (5227)Instruction limit reached!
% 3.08/1.64 % (5227)------------------------------
% 3.08/1.64 % (5227)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.64 % (5227)Termination reason: Unknown
% 3.08/1.64 % (5227)Termination phase: shuffling
% 3.08/1.64
% 3.08/1.64 % (5227)Memory used [KB]: 1407
% 3.08/1.64 % (5227)Time elapsed: 0.004 s
% 3.08/1.64 % (5227)Instructions burned: 8 (million)
% 3.08/1.64 % (5227)------------------------------
% 3.08/1.64 % (5227)------------------------------
% 3.08/1.64 % (5228)Instruction limit reached!
% 3.08/1.64 % (5228)------------------------------
% 3.08/1.64 % (5228)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.64 % (5228)Termination reason: Unknown
% 3.08/1.64 % (5228)Termination phase: shuffling
% 3.08/1.64
% 3.08/1.64 % (5228)Memory used [KB]: 1407
% 3.08/1.64 % (5228)Time elapsed: 0.003 s
% 3.08/1.64 % (5228)Instructions burned: 7 (million)
% 3.08/1.64 % (5228)------------------------------
% 3.08/1.64 % (5228)------------------------------
% 3.08/1.64 % (5226)Instruction limit reached!
% 3.08/1.64 % (5226)------------------------------
% 3.08/1.64 % (5226)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.64 % (5226)Termination reason: Unknown
% 3.08/1.64 % (5226)Termination phase: shuffling
% 3.08/1.64
% 3.08/1.64 % (5226)Memory used [KB]: 1663
% 3.08/1.64 % (5226)Time elapsed: 0.009 s
% 3.08/1.64 % (5226)Instructions burned: 22 (million)
% 3.08/1.64 % (5226)------------------------------
% 3.08/1.64 % (5226)------------------------------
% 3.08/1.65 % (5231)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_5010 for (2999ds/377Mi)
% 3.08/1.65 % (5235)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_5010 for (2999ds/779Mi)
% 3.08/1.65 % (5236)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_5010 for (2999ds/19Mi)
% 3.08/1.65 % (5237)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_5010 for (2999ds/879Mi)
% 3.08/1.66 % (5236)Instruction limit reached!
% 3.08/1.66 % (5236)------------------------------
% 3.08/1.66 % (5236)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.66 % (5236)Termination reason: Unknown
% 3.08/1.66 % (5236)Termination phase: shuffling
% 3.08/1.66
% 3.08/1.66 % (5236)Memory used [KB]: 1663
% 3.08/1.66 % (5236)Time elapsed: 0.007 s
% 3.08/1.66 % (5236)Instructions burned: 21 (million)
% 3.08/1.66 % (5236)------------------------------
% 3.08/1.66 % (5236)------------------------------
% 3.08/1.67 % (5238)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_5010 for (2999ds/17Mi)
% 3.08/1.67 % (5238)Instruction limit reached!
% 3.08/1.67 % (5238)------------------------------
% 3.08/1.67 % (5238)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.67 % (5238)Termination reason: Unknown
% 3.08/1.67 % (5238)Termination phase: shuffling
% 3.08/1.67
% 3.08/1.67 % (5238)Memory used [KB]: 1663
% 3.08/1.67 % (5238)Time elapsed: 0.007 s
% 3.08/1.67 % (5238)Instructions burned: 18 (million)
% 3.08/1.67 % (5238)------------------------------
% 3.08/1.67 % (5238)------------------------------
% 3.08/1.68 % (5239)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_5010 for (2998ds/3Mi)
% 3.08/1.68 % (5239)Instruction limit reached!
% 3.08/1.68 % (5239)------------------------------
% 3.08/1.68 % (5239)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.68 % (5239)Termination reason: Unknown
% 3.08/1.68 % (5239)Termination phase: shuffling
% 3.08/1.68
% 3.08/1.68 % (5239)Memory used [KB]: 1407
% 3.08/1.68 % (5239)Time elapsed: 0.002 s
% 3.08/1.68 % (5239)Instructions burned: 3 (million)
% 3.08/1.68 % (5239)------------------------------
% 3.08/1.68 % (5239)------------------------------
% 3.08/1.69 % (5240)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_5010 for (2998ds/30Mi)
% 3.08/1.70 % (5240)Instruction limit reached!
% 3.08/1.70 % (5240)------------------------------
% 3.08/1.70 % (5240)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.70 % (5240)Termination reason: Unknown
% 3.08/1.70 % (5240)Termination phase: shuffling
% 3.08/1.70
% 3.08/1.70 % (5240)Memory used [KB]: 1918
% 3.08/1.70 % (5240)Time elapsed: 0.011 s
% 3.08/1.70 % (5240)Instructions burned: 31 (million)
% 3.08/1.70 % (5240)------------------------------
% 3.08/1.70 % (5240)------------------------------
% 3.08/1.71 % (5244)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_5010 for (2998ds/127Mi)
% 3.08/1.75 % (5244)Instruction limit reached!
% 3.08/1.75 % (5244)------------------------------
% 3.08/1.75 % (5244)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.75 % (5244)Termination reason: Unknown
% 3.08/1.75 % (5244)Termination phase: Property scanning
% 3.08/1.75
% 3.08/1.75 % (5244)Memory used [KB]: 2302
% 3.08/1.75 % (5244)Time elapsed: 0.043 s
% 3.08/1.75 % (5244)Instructions burned: 127 (million)
% 3.08/1.75 % (5244)------------------------------
% 3.08/1.75 % (5244)------------------------------
% 3.08/1.76 % (5256)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_5010 for (2998ds/100Mi)
% 3.08/1.77 % (5231)Instruction limit reached!
% 3.08/1.77 % (5231)------------------------------
% 3.08/1.77 % (5231)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.77 % (5231)Termination reason: Unknown
% 3.08/1.77 % (5231)Termination phase: Saturation
% 3.08/1.77
% 3.08/1.77 % (5231)Memory used [KB]: 7675
% 3.08/1.77 % (5231)Time elapsed: 0.121 s
% 3.08/1.77 % (5231)Instructions burned: 378 (million)
% 3.08/1.77 % (5231)------------------------------
% 3.08/1.77 % (5231)------------------------------
% 3.08/1.78 % (5259)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_5010 for (2997ds/3Mi)
% 3.08/1.78 % (5259)Instruction limit reached!
% 3.08/1.78 % (5259)------------------------------
% 3.08/1.78 % (5259)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.78 % (5259)Termination reason: Unknown
% 3.08/1.78 % (5259)Termination phase: shuffling
% 3.08/1.78
% 3.08/1.78 % (5259)Memory used [KB]: 1407
% 3.08/1.78 % (5259)Time elapsed: 0.004 s
% 3.08/1.78 % (5259)Instructions burned: 4 (million)
% 3.08/1.78 % (5259)------------------------------
% 3.08/1.78 % (5259)------------------------------
% 3.08/1.79 % (5256)Instruction limit reached!
% 3.08/1.79 % (5256)------------------------------
% 3.08/1.79 % (5256)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.79 % (5256)Termination reason: Unknown
% 3.08/1.79 % (5256)Termination phase: Property scanning
% 3.08/1.79
% 3.08/1.79 % (5256)Memory used [KB]: 2302
% 3.08/1.79 % (5256)Time elapsed: 0.031 s
% 3.08/1.79 % (5256)Instructions burned: 103 (million)
% 3.08/1.79 % (5256)------------------------------
% 3.08/1.79 % (5256)------------------------------
% 3.08/1.80 % (5264)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_5010 for (2997ds/20Mi)
% 3.08/1.81 % (5264)Instruction limit reached!
% 3.08/1.81 % (5264)------------------------------
% 3.08/1.81 % (5264)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.81 % (5264)Termination reason: Unknown
% 3.08/1.81 % (5264)Termination phase: shuffling
% 3.08/1.81
% 3.08/1.81 % (5264)Memory used [KB]: 1663
% 3.08/1.81 % (5264)Time elapsed: 0.008 s
% 3.08/1.81 % (5264)Instructions burned: 21 (million)
% 3.08/1.81 % (5264)------------------------------
% 3.08/1.81 % (5264)------------------------------
% 3.08/1.81 % (5268)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_5010 for (2997ds/86Mi)
% 3.08/1.82 % (5273)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_5010 for (2997ds/107Mi)
% 3.08/1.85 % (5268)Instruction limit reached!
% 3.08/1.85 % (5268)------------------------------
% 3.08/1.85 % (5268)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.85 % (5268)Termination reason: Unknown
% 3.08/1.85 % (5268)Termination phase: Function definition elimination
% 3.08/1.85
% 3.08/1.85 % (5268)Memory used [KB]: 2302
% 3.08/1.85 % (5268)Time elapsed: 0.040 s
% 3.08/1.85 % (5268)Instructions burned: 88 (million)
% 3.08/1.85 % (5268)------------------------------
% 3.08/1.85 % (5268)------------------------------
% 3.08/1.86 % (5281)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_5010 for (2997ds/39Mi)
% 3.08/1.86 % (5273)Instruction limit reached!
% 3.08/1.86 % (5273)------------------------------
% 3.08/1.86 % (5273)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.86 % (5273)Termination reason: Unknown
% 3.08/1.86 % (5273)Termination phase: Property scanning
% 3.08/1.86
% 3.08/1.86 % (5273)Memory used [KB]: 2302
% 3.08/1.86 % (5273)Time elapsed: 0.041 s
% 3.08/1.86 % (5273)Instructions burned: 110 (million)
% 3.08/1.86 % (5273)------------------------------
% 3.08/1.86 % (5273)------------------------------
% 3.08/1.87 % (5281)Instruction limit reached!
% 3.08/1.87 % (5281)------------------------------
% 3.08/1.87 % (5281)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.87 % (5281)Termination reason: Unknown
% 3.08/1.87 % (5281)Termination phase: shuffling
% 3.08/1.87
% 3.08/1.87 % (5281)Memory used [KB]: 2174
% 3.08/1.87 % (5281)Time elapsed: 0.013 s
% 3.08/1.87 % (5281)Instructions burned: 41 (million)
% 3.08/1.87 % (5281)------------------------------
% 3.08/1.87 % (5281)------------------------------
% 3.08/1.87 % (5282)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_5010 for (2996ds/448Mi)
% 3.08/1.88 % (5283)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_5010 for (2996ds/46Mi)
% 3.08/1.89 % (5283)Instruction limit reached!
% 3.08/1.89 % (5283)------------------------------
% 3.08/1.89 % (5283)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.89 % (5283)Termination reason: Unknown
% 3.08/1.89 % (5283)Termination phase: SInE selection
% 3.08/1.89
% 3.08/1.89 % (5283)Memory used [KB]: 1918
% 3.08/1.89 % (5283)Time elapsed: 0.016 s
% 3.08/1.89 % (5283)Instructions burned: 47 (million)
% 3.08/1.89 % (5283)------------------------------
% 3.08/1.89 % (5283)------------------------------
% 3.08/1.89 % (5223)Instruction limit reached!
% 3.08/1.89 % (5223)------------------------------
% 3.08/1.89 % (5223)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.89 % (5223)Termination reason: Unknown
% 3.08/1.89 % (5223)Termination phase: Saturation
% 3.08/1.89
% 3.08/1.89 % (5223)Memory used [KB]: 7931
% 3.08/1.89 % (5223)Time elapsed: 0.262 s
% 3.08/1.89 % (5223)Instructions burned: 713 (million)
% 3.08/1.89 % (5223)------------------------------
% 3.08/1.89 % (5223)------------------------------
% 3.08/1.90 % (5284)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_5010 for (2996ds/98Mi)
% 3.08/1.90 % (5285)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_5010 for (2996ds/507Mi)
% 3.08/1.91 % (5235)Instruction limit reached!
% 3.08/1.91 % (5235)------------------------------
% 3.08/1.91 % (5235)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.91 % (5235)Termination reason: Unknown
% 3.08/1.91 % (5235)Termination phase: Saturation
% 3.08/1.91
% 3.08/1.91 % (5235)Memory used [KB]: 8059
% 3.08/1.91 % (5235)Time elapsed: 0.265 s
% 3.08/1.91 % (5235)Instructions burned: 782 (million)
% 3.08/1.91 % (5235)------------------------------
% 3.08/1.91 % (5235)------------------------------
% 3.08/1.92 % (5286)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_5010 for (2996ds/149Mi)
% 3.08/1.93 % (5284)Instruction limit reached!
% 3.08/1.93 % (5284)------------------------------
% 3.08/1.93 % (5284)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.93 % (5284)Termination reason: Unknown
% 3.08/1.93 % (5284)Termination phase: Property scanning
% 3.08/1.93
% 3.08/1.93 % (5284)Memory used [KB]: 2302
% 3.08/1.93 % (5284)Time elapsed: 0.027 s
% 3.08/1.93 % (5284)Instructions burned: 98 (million)
% 3.08/1.93 % (5284)------------------------------
% 3.08/1.93 % (5284)------------------------------
% 3.08/1.94 % (5287)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_5010 for (2996ds/39Mi)
% 3.08/1.94 % (5225)Instruction limit reached!
% 3.08/1.94 % (5225)------------------------------
% 3.08/1.94 % (5225)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.94 % (5225)Termination reason: Unknown
% 3.08/1.94 % (5225)Termination phase: Saturation
% 3.08/1.94
% 3.08/1.94 % (5225)Memory used [KB]: 8059
% 3.08/1.94 % (5225)Time elapsed: 0.315 s
% 3.08/1.94 % (5225)Instructions burned: 902 (million)
% 3.08/1.94 % (5225)------------------------------
% 3.08/1.94 % (5225)------------------------------
% 3.08/1.94 % (5237)First to succeed.
% 3.08/1.95 % (5237)Refutation found. Thanks to Tanya!
% 3.08/1.95 % SZS status Theorem for DTF2THF_5010
% 3.08/1.95 % SZS output start Proof for DTF2THF_5010
% 3.08/1.95 thf(type_def_5, type, secrecy_specID: $tType).
% 3.08/1.95 thf(type_def_6, type, secrecy_KS: $tType).
% 3.08/1.95 thf(type_def_7, type, set: ($tType) > $tType).
% 3.08/1.95 thf(type_def_9, type, list: ($tType) > $tType).
% 3.08/1.95 thf(type_def_10, type, secrecy_Expression: $tType).
% 3.08/1.95 thf(type_def_11, type, secrecy_chanID: $tType).
% 3.08/1.95 thf(type_def_12, type, secrecy_Keys: $tType).
% 3.08/1.95 thf(type_def_13, type, secrecy_Secrets: $tType).
% 3.08/1.95 thf(type_def_14, type, nat: $tType).
% 3.08/1.95 thf(func_def_0, type, secrecy_Expression: $tType).
% 3.08/1.95 thf(func_def_1, type, secrecy_Secrets: $tType).
% 3.08/1.95 thf(func_def_2, type, secrecy_specID: $tType).
% 3.08/1.95 thf(func_def_3, type, secrecy_chanID: $tType).
% 3.08/1.95 thf(func_def_4, type, secrecy_Keys: $tType).
% 3.08/1.95 thf(func_def_5, type, secrecy_KS: $tType).
% 3.08/1.95 thf(func_def_6, type, list: ($tType) > $tType).
% 3.08/1.95 thf(func_def_7, type, set: ($tType) > $tType).
% 3.08/1.95 thf(func_def_8, type, nat: $tType).
% 3.08/1.95 thf(func_def_9, type, bounded_lattice: !>[X0: $tType]:($o)).
% 3.08/1.95 thf(func_def_10, type, type: !>[X0: $tType]:($o)).
% 3.08/1.95 thf(func_def_11, type, bot: !>[X0: $tType]:($o)).
% 3.08/1.95 thf(func_def_12, type, ord: !>[X0: $tType]:($o)).
% 3.08/1.95 thf(func_def_13, type, order: !>[X0: $tType]:($o)).
% 3.08/1.95 thf(func_def_14, type, linorder: !>[X0: $tType]:($o)).
% 3.08/1.95 thf(func_def_15, type, preorder: !>[X0: $tType]:($o)).
% 3.08/1.95 thf(func_def_16, type, order_bot: !>[X0: $tType]:($o)).
% 3.08/1.95 thf(func_def_17, type, bounde1808546759up_bot: !>[X0: $tType]:($o)).
% 3.08/1.95 thf(func_def_18, type, localSecrets: secrecy_specID > set @ secrecy_KS).
% 3.08/1.95 thf(func_def_19, type, knowle1667810483orrect: secrecy_specID > secrecy_KS > $o).
% 3.08/1.95 thf(func_def_20, type, knowle1437066798e_know: secrecy_specID > secrecy_KS > $o).
% 3.08/1.95 thf(func_def_21, type, sup_sup: !>[X0: $tType]:(X0 > X0 > X0)).
% 3.08/1.95 thf(func_def_22, type, mem: !>[X0: $tType]:(X0 > list @ X0 > $o)).
% 3.08/1.95 thf(func_def_23, type, bot_bot: !>[X0: $tType]:(X0)).
% 3.08/1.95 thf(func_def_24, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 3.08/1.95 thf(func_def_25, type, correctCompositionKS: secrecy_specID > $o).
% 3.08/1.95 thf(func_def_26, type, correc17873122onKeys: secrecy_specID > $o).
% 3.08/1.95 thf(func_def_27, type, eout: secrecy_specID > secrecy_Expression > $o).
% 3.08/1.95 thf(func_def_28, type, eoutM: secrecy_specID > set @ secrecy_chanID > secrecy_Expression > $o).
% 3.08/1.95 thf(func_def_29, type, exprChannel: secrecy_chanID > secrecy_Expression > $o).
% 3.08/1.95 thf(func_def_30, type, ine: secrecy_specID > secrecy_Expression > $o).
% 3.08/1.95 thf(func_def_31, type, ineM: secrecy_specID > set @ secrecy_chanID > secrecy_Expression > $o).
% 3.08/1.95 thf(func_def_32, type, ine_exprChannelSet: secrecy_specID > set @ secrecy_chanID > secrecy_Expression > $o).
% 3.08/1.95 thf(func_def_33, type, ine_ex1303305700Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o).
% 3.08/1.95 thf(func_def_34, type, notSpe1586871396tsExpr: secrecy_specID > list @ secrecy_Expression > $o).
% 3.08/1.95 thf(func_def_35, type, out_exprChannelSet: secrecy_specID > set @ secrecy_chanID > secrecy_Expression > $o).
% 3.08/1.95 thf(func_def_36, type, out_ex985543062Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o).
% 3.08/1.95 thf(func_def_37, type, specKeys: secrecy_specID > set @ secrecy_Keys).
% 3.08/1.95 thf(func_def_38, type, specKeysSecrets: secrecy_specID > set @ secrecy_KS).
% 3.08/1.95 thf(func_def_39, type, specSecrets: secrecy_specID > set @ secrecy_Secrets).
% 3.08/1.95 thf(func_def_40, type, secrecy_kE: secrecy_Keys > secrecy_Expression).
% 3.08/1.95 thf(func_def_41, type, secrecy_sE: secrecy_Secrets > secrecy_Expression).
% 3.08/1.95 thf(func_def_42, type, secrec1016742679ession: secrecy_KS > secrecy_Expression).
% 3.08/1.95 thf(func_def_43, type, secrecy_kKS: secrecy_Keys > secrecy_KS).
% 3.08/1.95 thf(func_def_44, type, secrecy_sKS: secrecy_Secrets > secrecy_KS).
% 3.08/1.95 thf(func_def_45, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 3.08/1.95 thf(func_def_46, type, insert: !>[X0: $tType]:(X0 > set @ X0 > set @ X0)).
% 3.08/1.95 thf(func_def_47, type, is_empty: !>[X0: $tType]:(set @ X0 > $o)).
% 3.08/1.95 thf(func_def_48, type, is_singleton: !>[X0: $tType]:(set @ X0 > $o)).
% 3.08/1.95 thf(func_def_49, type, the_elem: !>[X0: $tType]:(set @ X0 > X0)).
% 3.08/1.95 thf(func_def_50, type, correctCompositionIn: secrecy_specID > $o).
% 3.08/1.95 thf(func_def_51, type, correc965049635ionLoc: secrecy_specID > $o).
% 3.08/1.95 thf(func_def_52, type, correc990227761ionOut: secrecy_specID > $o).
% 3.08/1.95 thf(func_def_53, type, inStream: secrecy_specID > set @ secrecy_chanID > $o).
% 3.08/1.95 thf(func_def_54, type, ins: secrecy_specID > set @ secrecy_chanID).
% 3.08/1.95 thf(func_def_55, type, loc: secrecy_specID > set @ secrecy_chanID).
% 3.08/1.95 thf(func_def_56, type, locStream: secrecy_specID > set @ secrecy_chanID > $o).
% 3.08/1.95 thf(func_def_57, type, out: secrecy_specID > set @ secrecy_chanID).
% 3.08/1.95 thf(func_def_58, type, subcomponents: secrecy_specID > set @ secrecy_specID).
% 3.08/1.95 thf(func_def_59, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 3.08/1.95 thf(func_def_60, type, p: secrecy_specID).
% 3.08/1.95 thf(func_def_61, type, pq: secrecy_specID).
% 3.08/1.95 thf(func_def_62, type, q: secrecy_specID).
% 3.08/1.95 thf(func_def_63, type, key: secrecy_Keys).
% 3.08/1.95 thf(func_def_64, type, m: secrecy_KS).
% 3.08/1.95 thf(func_def_80, type, sK0: secrecy_Keys > secrecy_specID > secrecy_chanID).
% 3.08/1.95 thf(func_def_81, type, sK1: secrecy_Keys > secrecy_specID > secrecy_chanID).
% 3.08/1.95 thf(func_def_82, type, sK2: secrecy_Secrets > secrecy_specID > secrecy_chanID).
% 3.08/1.95 thf(func_def_83, type, sK3: secrecy_KS > secrecy_specID > secrecy_specID > secrecy_Keys).
% 3.08/1.95 thf(func_def_84, type, sK4: secrecy_KS > secrecy_specID > secrecy_specID > secrecy_Secrets).
% 3.08/1.95 thf(func_def_85, type, sK5: secrecy_Secrets > secrecy_specID > secrecy_chanID).
% 3.08/1.95 thf(func_def_86, type, sK6: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 3.08/1.95 thf(func_def_88, type, ph8: !>[X0: $tType]:(X0)).
% 3.08/1.95 thf(f1827,plain,(
% 3.08/1.95 $false),
% 3.08/1.95 inference(subsumption_resolution,[status(thm)],[f1826,f918])).
% 3.08/1.95 thf(f918,plain,(
% 3.08/1.95 ($true != (member @ secrecy_KS @ (secrecy_kKS @ key) @ (specKeysSecrets @ p)))),
% 3.08/1.95 inference(definition_unfolding,[status(thm)],[f896,f914])).
% 3.08/1.95 thf(f914,plain,(
% 3.08/1.95 (m = (secrecy_kKS @ key))),
% 3.08/1.95 inference(cnf_transformation,[status(thm)],[f7])).
% 3.08/1.95 thf(f7,axiom,(
% 3.08/1.95 (m = (secrecy_kKS @ key))),
% 3.08/1.95 file('/export/starexec/sandbox/tmp/tmp.OaDn1w6qtU/DTF2THF_5010.p',fact_6_a1)).
% 3.08/1.95 thf(f896,plain,(
% 3.08/1.95 ((member @ secrecy_KS @ m @ (specKeysSecrets @ p)) != $true)),
% 3.08/1.95 inference(cnf_transformation,[status(thm)],[f817])).
% 3.08/1.95 thf(f817,plain,(
% 3.08/1.95 ((member @ secrecy_KS @ m @ (specKeysSecrets @ p)) != $true)),
% 3.08/1.95 inference(flattening,[status(thm)],[f571])).
% 3.08/1.95 thf(f571,plain,(
% 3.08/1.95 ~((member @ secrecy_KS @ m @ (specKeysSecrets @ p)) = $true)),
% 3.08/1.95 inference(fool_elimination,[status(thm)],[f570])).
% 3.08/1.95 thf(f570,plain,(
% 3.08/1.95 ~(member @ secrecy_KS @ m @ (specKeysSecrets @ p))),
% 3.08/1.95 inference(rectify,[status(thm)],[f3])).
% 3.08/1.95 thf(f3,axiom,(
% 3.08/1.95 ~(member @ secrecy_KS @ m @ (specKeysSecrets @ p))),
% 3.08/1.95 file('/export/starexec/sandbox/tmp/tmp.OaDn1w6qtU/DTF2THF_5010.p',fact_2_notKSP)).
% 3.08/1.95 thf(f1826,plain,(
% 3.08/1.95 ($true = (member @ secrecy_KS @ (secrecy_kKS @ key) @ (specKeysSecrets @ p)))),
% 3.08/1.95 inference(subsumption_resolution,[status(thm)],[f1825,f891])).
% 3.08/1.95 thf(f891,plain,(
% 3.08/1.95 ((correctCompositionKS @ pq) = $true)),
% 3.08/1.95 inference(cnf_transformation,[status(thm)],[f717])).
% 3.08/1.95 thf(f717,plain,(
% 3.08/1.95 ((correctCompositionKS @ pq) = $true)),
% 3.08/1.95 inference(fool_elimination,[status(thm)],[f716])).
% 3.08/1.95 thf(f716,plain,(
% 3.08/1.95 (correctCompositionKS @ pq)),
% 3.08/1.95 inference(rectify,[status(thm)],[f1])).
% 3.08/1.95 thf(f1,axiom,(
% 3.08/1.95 (correctCompositionKS @ pq)),
% 3.08/1.95 file('/export/starexec/sandbox/tmp/tmp.OaDn1w6qtU/DTF2THF_5010.p',fact_0_cCompKS)).
% 3.08/1.95 thf(f1825,plain,(
% 3.08/1.95 ((correctCompositionKS @ pq) != $true) | ($true = (member @ secrecy_KS @ (secrecy_kKS @ key) @ (specKeysSecrets @ p)))),
% 3.08/1.95 inference(subsumption_resolution,[status(thm)],[f1824,f917])).
% 3.08/1.95 thf(f917,plain,(
% 3.08/1.95 ($true != (member @ secrecy_KS @ (secrecy_kKS @ key) @ (specKeysSecrets @ q)))),
% 3.08/1.95 inference(definition_unfolding,[status(thm)],[f887,f914])).
% 3.08/1.95 thf(f887,plain,(
% 3.08/1.95 ((member @ secrecy_KS @ m @ (specKeysSecrets @ q)) != $true)),
% 3.08/1.95 inference(cnf_transformation,[status(thm)],[f814])).
% 3.08/1.95 thf(f814,plain,(
% 3.08/1.95 ((member @ secrecy_KS @ m @ (specKeysSecrets @ q)) != $true)),
% 3.08/1.95 inference(flattening,[status(thm)],[f645])).
% 3.08/1.95 thf(f645,plain,(
% 3.08/1.95 ~((member @ secrecy_KS @ m @ (specKeysSecrets @ q)) = $true)),
% 3.08/1.95 inference(fool_elimination,[status(thm)],[f644])).
% 3.08/1.95 thf(f644,plain,(
% 3.08/1.95 ~(member @ secrecy_KS @ m @ (specKeysSecrets @ q))),
% 3.08/1.95 inference(rectify,[status(thm)],[f2])).
% 3.08/1.95 thf(f2,axiom,(
% 3.08/1.95 ~(member @ secrecy_KS @ m @ (specKeysSecrets @ q))),
% 3.08/1.95 file('/export/starexec/sandbox/tmp/tmp.OaDn1w6qtU/DTF2THF_5010.p',fact_1_notKSQ)).
% 3.08/1.95 thf(f1824,plain,(
% 3.08/1.95 ($true = (member @ secrecy_KS @ (secrecy_kKS @ key) @ (specKeysSecrets @ q))) | ((correctCompositionKS @ pq) != $true) | ($true = (member @ secrecy_KS @ (secrecy_kKS @ key) @ (specKeysSecrets @ p)))),
% 3.08/1.95 inference(trivial_inequality_removal,[status(thm)],[f1823])).
% 3.08/1.95 thf(f1823,plain,(
% 3.08/1.95 ($true = (member @ secrecy_KS @ (secrecy_kKS @ key) @ (specKeysSecrets @ p))) | ($true != $true) | ($true = (member @ secrecy_KS @ (secrecy_kKS @ key) @ (specKeysSecrets @ q))) | ((subcomponents @ pq) != (subcomponents @ pq)) | ((correctCompositionKS @ pq) != $true)),
% 3.08/1.95 inference(superposition,[status(thm)],[f1076,f919])).
% 3.08/1.95 thf(f919,plain,(
% 3.08/1.95 ($true = (member @ secrecy_KS @ (secrecy_kKS @ key) @ (specKeysSecrets @ pq)))),
% 3.08/1.95 inference(definition_unfolding,[status(thm)],[f911,f914])).
% 3.08/1.95 thf(f911,plain,(
% 3.08/1.95 ((member @ secrecy_KS @ m @ (specKeysSecrets @ pq)) = $true)),
% 3.08/1.95 inference(cnf_transformation,[status(thm)],[f810])).
% 3.08/1.95 thf(f810,plain,(
% 3.08/1.95 ((member @ secrecy_KS @ m @ (specKeysSecrets @ pq)) = $true)),
% 3.08/1.95 inference(flattening,[status(thm)],[f419])).
% 3.08/1.95 thf(f419,plain,(
% 3.08/1.95 ~~((member @ secrecy_KS @ m @ (specKeysSecrets @ pq)) = $true)),
% 3.08/1.95 inference(fool_elimination,[status(thm)],[f418])).
% 3.08/1.95 thf(f418,plain,(
% 3.08/1.95 ~~(member @ secrecy_KS @ m @ (specKeysSecrets @ pq))),
% 3.08/1.95 inference(rectify,[status(thm)],[f286])).
% 3.08/1.95 thf(f286,negated_conjecture,(
% 3.08/1.95 ~~(member @ secrecy_KS @ m @ (specKeysSecrets @ pq))),
% 3.08/1.95 inference(negated_conjecture,[status(cth)],[f285])).
% 3.08/1.95 thf(f285,conjecture,(
% 3.08/1.95 ~(member @ secrecy_KS @ m @ (specKeysSecrets @ pq))),
% 3.08/1.95 file('/export/starexec/sandbox/tmp/tmp.OaDn1w6qtU/DTF2THF_5010.p',conj_0)).
% 3.08/1.95 thf(f1076,plain,(
% 3.08/1.95 ( ! [X0 : secrecy_specID,X1 : secrecy_KS] : (((member @ secrecy_KS @ X1 @ (specKeysSecrets @ X0)) != $true) | ($true = (member @ secrecy_KS @ X1 @ (specKeysSecrets @ p))) | ((subcomponents @ pq) != (subcomponents @ X0)) | ($true = (member @ secrecy_KS @ X1 @ (specKeysSecrets @ q))) | ((correctCompositionKS @ X0) != $true)) )),
% 3.08/1.95 inference(superposition,[status(thm)],[f889,f890])).
% 3.08/1.95 thf(f890,plain,(
% 3.08/1.95 ((subcomponents @ pq) = (insert @ secrecy_specID @ p @ (insert @ secrecy_specID @ q @ bot_bot @ set @ secrecy_specID)))),
% 3.08/1.95 inference(cnf_transformation,[status(thm)],[f4])).
% 3.08/1.95 thf(f4,axiom,(
% 3.08/1.95 ((subcomponents @ pq) = (insert @ secrecy_specID @ p @ (insert @ secrecy_specID @ q @ bot_bot @ set @ secrecy_specID)))),
% 3.08/1.95 file('/export/starexec/sandbox/tmp/tmp.OaDn1w6qtU/DTF2THF_5010.p',fact_3_subPQ)).
% 3.08/1.95 thf(f889,plain,(
% 3.08/1.95 ( ! [X2 : secrecy_specID,X3 : secrecy_KS,X0 : secrecy_specID,X1 : secrecy_specID] : (((insert @ secrecy_specID @ X1 @ (insert @ secrecy_specID @ X2 @ bot_bot @ set @ secrecy_specID)) != (subcomponents @ X0)) | ($true != (member @ secrecy_KS @ X3 @ (specKeysSecrets @ X0))) | ($true = (member @ secrecy_KS @ X3 @ (specKeysSecrets @ X2))) | ($true = (member @ secrecy_KS @ X3 @ (specKeysSecrets @ X1))) | ((correctCompositionKS @ X0) != $true)) )),
% 3.08/1.95 inference(cnf_transformation,[status(thm)],[f858])).
% 3.08/1.95 thf(f858,plain,(
% 3.08/1.95 ! [X0 : secrecy_specID,X1 : secrecy_specID,X2 : secrecy_specID,X3 : secrecy_KS] : (($true = (member @ secrecy_KS @ X3 @ (specKeysSecrets @ X1))) | ((correctCompositionKS @ X0) != $true) | ($true = (member @ secrecy_KS @ X3 @ (specKeysSecrets @ X2))) | ($true != (member @ secrecy_KS @ X3 @ (specKeysSecrets @ X0))) | ((insert @ secrecy_specID @ X1 @ (insert @ secrecy_specID @ X2 @ bot_bot @ set @ secrecy_specID)) != (subcomponents @ X0)))),
% 3.08/1.95 inference(flattening,[status(thm)],[f857])).
% 3.08/1.95 thf(f857,plain,(
% 3.08/1.95 ! [X0 : secrecy_specID,X1 : secrecy_specID,X2 : secrecy_specID,X3 : secrecy_KS] : ((((($true != (member @ secrecy_KS @ X3 @ (specKeysSecrets @ X0))) | ($true = (member @ secrecy_KS @ X3 @ (specKeysSecrets @ X2)))) | ($true = (member @ secrecy_KS @ X3 @ (specKeysSecrets @ X1)))) | ((correctCompositionKS @ X0) != $true)) | ((insert @ secrecy_specID @ X1 @ (insert @ secrecy_specID @ X2 @ bot_bot @ set @ secrecy_specID)) != (subcomponents @ X0)))),
% 3.08/1.95 inference(ennf_transformation,[status(thm)],[f825])).
% 3.08/1.95 thf(f825,plain,(
% 3.08/1.95 ! [X0 : secrecy_specID,X1 : secrecy_specID,X2 : secrecy_specID,X3 : secrecy_KS] : (((insert @ secrecy_specID @ X1 @ (insert @ secrecy_specID @ X2 @ bot_bot @ set @ secrecy_specID)) = (subcomponents @ X0)) => (((correctCompositionKS @ X0) = $true) => (($true != (member @ secrecy_KS @ X3 @ (specKeysSecrets @ X1))) => (($true != (member @ secrecy_KS @ X3 @ (specKeysSecrets @ X2))) => ($true != (member @ secrecy_KS @ X3 @ (specKeysSecrets @ X0)))))))),
% 3.08/1.95 inference(flattening,[status(thm)],[f395])).
% 3.08/1.95 thf(f395,plain,(
% 3.08/1.95 ! [X0 : secrecy_specID,X1 : secrecy_specID,X2 : secrecy_specID,X3 : secrecy_KS] : (((insert @ secrecy_specID @ X1 @ (insert @ secrecy_specID @ X2 @ bot_bot @ set @ secrecy_specID)) = (subcomponents @ X0)) => (((correctCompositionKS @ X0) = $true) => (~($true = (member @ secrecy_KS @ X3 @ (specKeysSecrets @ X1))) => (~($true = (member @ secrecy_KS @ X3 @ (specKeysSecrets @ X2))) => ~($true = (member @ secrecy_KS @ X3 @ (specKeysSecrets @ X0)))))))),
% 3.08/1.95 inference(fool_elimination,[status(thm)],[f394])).
% 3.08/1.95 thf(f394,plain,(
% 3.08/1.95 ! [X0 : secrecy_specID,X1 : secrecy_specID,X2 : secrecy_specID,X3 : secrecy_KS] : (((insert @ secrecy_specID @ X1 @ (insert @ secrecy_specID @ X2 @ bot_bot @ set @ secrecy_specID)) = (subcomponents @ X0)) => ((correctCompositionKS @ X0) => (~(member @ secrecy_KS @ X3 @ (specKeysSecrets @ X1)) => (~(member @ secrecy_KS @ X3 @ (specKeysSecrets @ X2)) => ~(member @ secrecy_KS @ X3 @ (specKeysSecrets @ X0))))))),
% 3.08/1.95 inference(rectify,[status(thm)],[f9])).
% 3.08/1.95 thf(f9,axiom,(
% 3.08/1.95 ! [X1 : secrecy_specID,X2 : secrecy_specID,X3 : secrecy_specID,X4 : secrecy_KS] : (((subcomponents @ X1) = (insert @ secrecy_specID @ X2 @ (insert @ secrecy_specID @ X3 @ bot_bot @ set @ secrecy_specID))) => ((correctCompositionKS @ X1) => (~(member @ secrecy_KS @ X4 @ (specKeysSecrets @ X2)) => (~(member @ secrecy_KS @ X4 @ (specKeysSecrets @ X3)) => ~(member @ secrecy_KS @ X4 @ (specKeysSecrets @ X1))))))),
% 3.08/1.95 file('/export/starexec/sandbox/tmp/tmp.OaDn1w6qtU/DTF2THF_5010.p',fact_8_correctCompositionKS__neg1)).
% 3.08/1.95 % SZS output end Proof for DTF2THF_5010
% 3.08/1.95 % (5237)------------------------------
% 3.08/1.95 % (5237)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.95 % (5237)Termination reason: Refutation
% 3.08/1.95
% 3.08/1.95 % (5237)Memory used [KB]: 7675
% 3.08/1.95 % (5237)Time elapsed: 0.295 s
% 3.08/1.95 % (5237)Instructions burned: 754 (million)
% 3.08/1.95 % (5237)------------------------------
% 3.08/1.95 % (5237)------------------------------
% 3.08/1.95 % (5202)Success in time 0.396 s
%------------------------------------------------------------------------------